numerical analysis research paper

• Search Menu
• Advance articles
• Author Guidelines
• Submission Site
• Open Access
• About IMA Journal of Numerical Analysis
• About the Institute of Mathematics and its Applications
• Editorial Board
• Advertising and Corporate Services
• Journals Career Network
• Self-Archiving Policy
• Dispatch Dates
• Journals on Oxford Academic
• Books on Oxford Academic

Prof. C.M. Elliott

Prof. A. Ern

Prof. A. Iserles

Prof. E. Süli

About the journal

The IMA Journal of Numerical Analysis (IMAJNA) publishes original contributions to all fields of numerical analysis; articles will be accepted which treat the theory, development or use of practical algorithms and interactions between these aspects …

Interested in submitting

Find out more about publishing in the IMA Journal of Numerical Analysis and submit today.

Find out more

Read and Publish deals

Authors interested in publishing in  IMA Journal of Numerical Analysis  may be able to publish their paper Open Access using funds available through their institution’s agreement with OUP.

Find out if your institution is participating

Read our step-by-step guide for accessing R&P funds

High-Impact Research Collection

Explore a collection of freely available high-impact research published in the  IMA Journal of Numerical Analysis  within the past two years.

Browse the collection here

Latest articles

Email alerts

Register to receive table of contents email alerts as soon as new issues of IMA Journal of Numerical Analysis are published online.

Recommend to your library

Fill out our simple online form to recommend IMA Journal of Numerical Analysis to your library.

Recommend now

Committee on Publication Ethics (COPE)

This journal is a member of and subscribes to the principles of the Committee on Publication Ethics (COPE)

publicationethics.org

Published on behalf of the IMA

This journal is published on behalf of the Institute of Mathematics and its Applications. All IMA journals encourage diversity.

Related Titles

• Recommend to your Library

Affiliations

• Online ISSN 1464-3642
• Print ISSN 0272-4979
• Copyright © 2024 Institute of Mathematics and its Applications
• About Oxford Academic
• Publish journals with us
• University press partners
• What we publish
• New features  
• Open access
• Institutional account management
• Rights and permissions
• Get help with access
• Accessibility
• Advertising
• Media enquiries
• Oxford University Press
• Oxford Languages
• University of Oxford

Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide

• Copyright © 2024 Oxford University Press
• Cookie settings
• Cookie policy
• Privacy policy
• Legal notice

This Feature Is Available To Subscribers Only

Sign In or Create an Account

This PDF is available to Subscribers Only

For full access to this pdf, sign in to an existing account, or purchase an annual subscription.

numerical analysis Recently Published Documents

Total documents.

• Latest Documents
• Most Cited Documents
• Contributed Authors
• Related Sources
• Related Keywords

Numerical analysis of layout of air conditioning in data center considering seasonal factors

Experimental and numerical analysis of fine particle and soot formation in a modern 100 mw pulverized biomass heating plant, numerical analysis of very rich propagating spherical flames: soot formation and its impact on the determination of laminar flame speed, numerical analysis of forced convection heat transfer in a nuclear fuel storage vault, numerical analysis of a high-order accurate compact finite difference scheme for the srlw equation, a modified mixture theory for one-dimensional melting of pure pcm and pcm/metal foam composite: numerical analysis and experiment validation, volume of fluid-based numerical analysis of a pump-driven phase change heat transport device, some biorthogonal polynomials arising in numerical analysis and approximation theory, numerical analysis of the thermal and hydraulic characteristics of co2/propane mixtures in printed circuit heat exchangers, numerical analysis of cooling performance of a novel structure affected by aeolian sand clogging on expressway embankment in permafrost regions, export citation format, share document.

> math > math.NA

Help | Advanced Search

Numerical Analysis

Authors and titles for recent submissions.

• Fri, 3 May 2024
• Thu, 2 May 2024
• Wed, 1 May 2024
• Tue, 30 Apr 2024
• Mon, 29 Apr 2024

Thu, 2 May 2024 (showing first 3 of 13 entries)

Links to: arXiv , form interface , find , math , new , 2405 , contact , h elp   ( Access key information)

Qualitative Analysis of a Novel Numerical Method for Solving Non-linear Ordinary Differential Equations

• Original Paper
• Published: 17 April 2024
• Volume 10 , article number  99 , ( 2024 )

Cite this article

• Sonali Kaushik 1 &
• Rajesh Kumar 2  

84 Accesses

Explore all metrics

The dynamics of innumerable real-world phenomena is represented with the help of non-linear ordinary differential equations (NODEs). There is a growing trend of solving these equations using accurate and easy to implement methods. The goal of this research work is to create a numerical method to solve the first-order NODEs (FNODEs) by coupling of the well-known trapezoidal method with a newly developed semi-analytical technique called the Laplace optimized decomposition method (LODM). The novelty of this coupling lies in the improvement of order of accuracy of the scheme when the terms in the series solution are increased. The article discusses the qualitative behavior of the new method, i.e., consistency, stability and convergence. Several numerical test cases of the non-linear differential equations are considered to validate our findings.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price includes VAT (Russian Federation)

Instant access to the full article PDF.

Rent this article via DeepDyve

Institutional subscriptions

Similar content being viewed by others

Existence Results for Positive Periodic Solutions to First-Order Neutral Differential Equations

$$\mathcal {h}_2$$ optimal rational approximation on general domains, first-order differential equations in chemistry, data availability.

Enquiries about data availability should be directed to the authors.

Simmons, G.F.: Differential Equations with Applications and Historical Notes. CRC Press, Boca Raton (2016)

Google Scholar  

Nagle, R.K., Saff, E.B., Snider, A.D.: Fundamentals of Differential Equations. Pearson, London (2017)

Nadeem, M., He, J.-H., He, C.-H., Sedighi, H.M., Shirazi, A.: A numerical solution of nonlinear fractional Newell-Whitehead-Segel equation using natural transform. TWMS J. Pure Appl. Math. 13 (2), 168–182 (2022)

Liu, J., Nadeem, M., Habib, M., Karim, S., Or Roshid, H.: Numerical investigation of the nonlinear coupled fractional massive thirring equation using two-scale approach, Complexity 2022 (2022)

Nadeem, M., He, J.-H., Islam, A.: The homotopy perturbation method for fractional differential equations: part 1 mohand transform. Int. J. Numer. Methods Heat Fluid Flow 31 (11), 3490–3504 (2021)

Article   Google Scholar  

Tran, T.V.H., Pavelková, D., Homolka, L.: Solow model with technological progress: an empirical study of economic growth in Vietnam through Ardl approach. Quality-Access to Success 23 (186) (2022)

Briec, W., Lasselle, L.: On some relations between a continuous time Luenberger productivity indicator and the Solow model. Bull. Econ. Res. 74 (2), 484–502 (2022)

Article   MathSciNet   Google Scholar  

Danca, M., Codreanu, S., Bako, B.: Detailed analysis of a nonlinear prey–predator model. J. Biol. Phys. 23 (1), 11 (1997)

Bentout, S., Djilali, S., Atangana, A.: Bifurcation analysis of an age-structured prey–predator model with infection developed in prey. Math. Methods Appl. Sci. 45 (3), 1189–1208 (2022)

Campos, L.: Non-Linear Differential Equations and Dynamical Systems: Ordinary Differential Equations with Applications to Trajectories and Oscillations. CRC Press, Boca Raton (2019)

Book   Google Scholar  

Shah, N.A., Ahmad, I., Bazighifan, O., Abouelregal, A.E., Ahmad, H.: Multistage optimal homotopy asymptotic method for the nonlinear Riccati ordinary differential equation in nonlinear physics. Appl. Math. 14 (6), 1009–1016 (2020)

MathSciNet   Google Scholar  

LeVeque, R.J.: Finite Difference Methods for Ordinary and Partial Differential Equations. Steady-state and Time-Dependent Problems. SIAM, Philadelphia (2007)

Mickens, R.E.: Nonstandard finite difference schemes for differential equations. J. Differ. Equ. Appl. 8 (9), 823–847 (2002)

Mehdizadeh Khalsaraei, M., Khodadosti, F.: Nonstandard finite difference schemes for differential equations. Sahand Commun. Math. Anal. 1 (2), 47–54 (2014)

Thirumalai, S., Seshadri, R., Yuzbasi, S.: Spectral solutions of fractional differential equations modelling combined drug therapy for HIV infection. Chaos, Solitons & Fractals 151 , 111234 (2021)

Evans, G.A., Blackledge, J.M., Yardley, P.D.: Finite element method for ordinary differential equations. In: Numerical Methods for Partial Differential Equations, pp. 123–164. Springer(2000)

Deng, K., Xiong, Z.: Superconvergence of a discontinuous finite element method for a nonlinear ordinary differential equation. Appl. Math. Comput. 217 (7), 3511–3515 (2010)

Wriggers, P.: Nonlinear Finite Element Methods. Springer, Berlin (2008)

Gonsalves, S., Swapna, G.: Finite element study of nanofluid through porous nonlinear stretching surface under convective boundary conditions. Mater. Today Proc. (2023)

Al-Omari, A., Schüttler, H.-B., Arnold, J., Taha, T.: Solving nonlinear systems of first order ordinary differential equations using a Galerkin finite element method. IEEE Access 1 , 408–417 (2013)

Odibat, Z.: An optimized decomposition method for nonlinear ordinary and partial differential equations. Phys. A 541 , 123323 (2020)

Jafari, H., Daftardar-Gejji, V.: Revised adomian decomposition method for solving systems of ordinary and fractional differential equations. Appl. Math. Comput. 181 (1), 598–608 (2006)

Liao, S.: Homotopy Analysis Method in Nonlinear Differential Equations. Springer, Berlin (2012)

Odibat, Z.: An improved optimal homotopy analysis algorithm for nonlinear differential equations. J. Math. Anal. Appl. 488 (2), 124089 (2020)

He, J.-H., Latifizadeh, H.: A general numerical algorithm for nonlinear differential equations by the variational iteration method. Int. J. Numer. Methods Heat Fluid Flow 30 (11), 4797–4810 (2020)

Biazar, J., Ghazvini, H.: He’s variational iteration method for solving linear and non-linear systems of ordinary differential equations. Appl. Math. Comput. 191 (1), 287–297 (2007)

Ramos, J.I.: On the variational iteration method and other iterative techniques for nonlinear differential equations. Appl. Math. Comput. 199 (1), 39–69 (2008)

Geng, F.: A modified variational iteration method for solving Riccati differential equations. Comput. Math. Appl. 60 (7), 1868–1872 (2010)

Kumar, R.V., Sarris, I.E., Sowmya, G., Abdulrahman, A.: Iterative solutions for the nonlinear heat transfer equation of a convective-radiative annular fin with power law temperature-dependent thermal properties. Symmetry 15 (6), 1204 (2023)

Sowmya, G., Kumar, R.S.V., Banu, Y.: Thermal performance of a longitudinal fin under the influence of magnetic field using sumudu transform method with pade approximant (stm-pa). ZAMM J. Appl. Math. Mech. 103 , e202100526 (2023)

Varun Kumar, R.S., Sowmya, G., Jayaprakash, M.C., Prasannakumara, B.C., Khan, M.I., Guedri, K., Kumam, P., Sitthithakerngkiet, K., Galal, A.M.: Assessment of thermal distribution through an inclined radiative–convective porous fin of concave profile using generalized residual power series method (GRPSM). Sci. Rep. (2022). https://doi.org/10.1038/s41598-022-15396-z

Kaushik, S., Kumar, R.: A novel optimized decomposition method for Smoluchowski’s aggregation equation. J. Comput. Appl. Math. 419 , 114710 (2023)

Odibat, Z.: The optimized decomposition method for a reliable treatment of ivps for second order differential equations. Phys. Scr. 96 (9), 095206 (2021)

Beghami, W., Maayah, B., Bushnaq, S., Abu Arqub, O.: The laplace optimized decomposition method for solving systems of partial differential equations of fractional order. Int. J. Appl. Comput. Math. 8 , 52 (2022). https://doi.org/10.1007/s40819-022-01256-x

Kaushik, S., Hussain, S., Kumar, R.: Laplace transform-based approximation methods for solving pure aggregation and breakage equations. Math. Methods Appl. Sci. 46 (16), 17402–17421 (2023)

Patade, J., Bhalekar, S.: A new numerical method based on Daftardar-Gejji and Jafari technique for solving differential equations. World J. Model. Simul. 11 , 256–271 (2015)

Patade, J., Bhalekar, S.: A novel numerical method for solving Volterra integro-differential equations. Int. J. Appl. Comput. Math. 6 (1), 1–19 (2020)

Ali, L., Islam, S., Gul, T., Amiri, I.S.: Solution of nonlinear problems by a new analytical technique using Daftardar-Gejji and Jafari polynomials. Adv. Mech. Eng. 11 (12), 1687814019896962 (2019)

Download references

Rajesh Kumar wishes to thank Science and Engineering Research Board (SERB), Department of Science and Technology (DST), India, for the funding through the project MTR/2021/000866.

Author information

Authors and affiliations.

Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati, 522237, India

Sonali Kaushik

Department of Mathematics, BITS Pilani, Pilani Campus, Pilani, Rajasthan, 333031, India

Rajesh Kumar

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Sonali Kaushik .

Ethics declarations

Competing interests.

The authors have not disclosed any competing interests.

Additional information

Publisher's note.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Kaushik, S., Kumar, R. Qualitative Analysis of a Novel Numerical Method for Solving Non-linear Ordinary Differential Equations. Int. J. Appl. Comput. Math 10 , 99 (2024). https://doi.org/10.1007/s40819-024-01735-3

Download citation

Accepted : 27 March 2024

Published : 17 April 2024

DOI : https://doi.org/10.1007/s40819-024-01735-3

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• First-order non-linear differential equations
• Trapezoidal method
• Semi-analytical method
• Laplace transform
• Laplace optimized decomposition method
• Consistency
• Convergence

Mathematics Subject Classification

• Primary 45K05
• Secondary 34A34
• Find a journal
• Publish with us
• Track your research

• USC Libraries
• Research Guides

Organizing Your Social Sciences Research Paper

• Quantitative Methods
• Purpose of Guide
• Design Flaws to Avoid
• Independent and Dependent Variables
• Glossary of Research Terms
• Reading Research Effectively
• Narrowing a Topic Idea
• Broadening a Topic Idea
• Extending the Timeliness of a Topic Idea
• Academic Writing Style
• Applying Critical Thinking
• Choosing a Title
• Making an Outline
• Paragraph Development
• Research Process Video Series
• Executive Summary
• The C.A.R.S. Model
• Background Information
• The Research Problem/Question
• Theoretical Framework
• Citation Tracking
• Content Alert Services
• Evaluating Sources
• Primary Sources
• Secondary Sources
• Tiertiary Sources
• Scholarly vs. Popular Publications
• Qualitative Methods
• Insiderness
• Using Non-Textual Elements
• Limitations of the Study
• Common Grammar Mistakes
• Writing Concisely
• Avoiding Plagiarism
• Footnotes or Endnotes?
• Further Readings
• Generative AI and Writing
• USC Libraries Tutorials and Other Guides
• Bibliography

Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Muijs, Daniel. Doing Quantitative Research in Education with SPSS . 2nd edition. London: SAGE Publications, 2010.

Need Help Locating Statistics?

Resources for locating data and statistics can be found here:

Statistics & Data Research Guide

Characteristics of Quantitative Research

Your goal in conducting quantitative research study is to determine the relationship between one thing [an independent variable] and another [a dependent or outcome variable] within a population. Quantitative research designs are either descriptive [subjects usually measured once] or experimental [subjects measured before and after a treatment]. A descriptive study establishes only associations between variables; an experimental study establishes causality.

Quantitative research deals in numbers, logic, and an objective stance. Quantitative research focuses on numeric and unchanging data and detailed, convergent reasoning rather than divergent reasoning [i.e., the generation of a variety of ideas about a research problem in a spontaneous, free-flowing manner].

Its main characteristics are :

• The data is usually gathered using structured research instruments.
• The results are based on larger sample sizes that are representative of the population.
• The research study can usually be replicated or repeated, given its high reliability.
• Researcher has a clearly defined research question to which objective answers are sought.
• All aspects of the study are carefully designed before data is collected.
• Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
• Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
• Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

  Things to keep in mind when reporting the results of a study using quantitative methods :

• Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
• Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data and why any missing data does not undermine the validity of your analysis.
• Explain the techniques you used to "clean" your data set.
• Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
• Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
• When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level [report the actual p value].
• Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
• Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
• Always tell the reader what to look for in tables and figures .

NOTE:   When using pre-existing statistical data gathered and made available by anyone other than yourself [e.g., government agency], you still must report on the methods that were used to gather the data and describe any missing data that exists and, if there is any, provide a clear explanation why the missing data does not undermine the validity of your final analysis.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods. Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Design for Quantitative Studies

Before designing a quantitative research study, you must decide whether it will be descriptive or experimental because this will dictate how you gather, analyze, and interpret the results. A descriptive study is governed by the following rules: subjects are generally measured once; the intention is to only establish associations between variables; and, the study may include a sample population of hundreds or thousands of subjects to ensure that a valid estimate of a generalized relationship between variables has been obtained. An experimental design includes subjects measured before and after a particular treatment, the sample population may be very small and purposefully chosen, and it is intended to establish causality between variables. Introduction The introduction to a quantitative study is usually written in the present tense and from the third person point of view. It covers the following information:

• Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
• Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
• Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Methodology The methods section of a quantitative study should describe how each objective of your study will be achieved. Be sure to provide enough detail to enable the reader can make an informed assessment of the methods being used to obtain results associated with the research problem. The methods section should be presented in the past tense.

• Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
• Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
• Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.

Results The finding of your study should be written objectively and in a succinct and precise format. In quantitative studies, it is common to use graphs, tables, charts, and other non-textual elements to help the reader understand the data. Make sure that non-textual elements do not stand in isolation from the text but are being used to supplement the overall description of the results and to help clarify key points being made. Further information about how to effectively present data using charts and graphs can be found here .

• Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.

Discussion Discussions should be analytic, logical, and comprehensive. The discussion should meld together your findings in relation to those identified in the literature review, and placed within the context of the theoretical framework underpinning the study. The discussion should be presented in the present tense.

• Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
• Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
• Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
• Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.

• Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
• Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
• Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.

Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics . London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications . 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Composition and TESOL . Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); "A Strategy for Writing Up Research Results. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper." Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research . Kennesaw State University.

Strengths of Using Quantitative Methods

Quantitative researchers try to recognize and isolate specific variables contained within the study framework, seek correlation, relationships and causality, and attempt to control the environment in which the data is collected to avoid the risk of variables, other than the one being studied, accounting for the relationships identified.

Among the specific strengths of using quantitative methods to study social science research problems:

• Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
• Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
• Applying well established standards means that the research can be replicated, and then analyzed and compared with similar studies;
• You can summarize vast sources of information and make comparisons across categories and over time; and,
• Personal bias can be avoided by keeping a 'distance' from participating subjects and using accepted computational techniques .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Limitations of Using Quantitative Methods

Quantitative methods presume to have an objective approach to studying research problems, where data is controlled and measured, to address the accumulation of facts, and to determine the causes of behavior. As a consequence, the results of quantitative research may be statistically significant but are often humanly insignificant.

Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:

• Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
• Uses a static and rigid approach and so employs an inflexible process of discovery;
• The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
• Results provide less detail on behavior, attitudes, and motivation;
• Researcher may collect a much narrower and sometimes superficial dataset;
• Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
• The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
• Preset answers will not necessarily reflect how people really feel about a subject and, in some cases, might just be the closest match to the preconceived hypothesis.

Research Tip

Finding Examples of How to Apply Different Types of Research Methods

SAGE publications is a major publisher of studies about how to design and conduct research in the social and behavioral sciences. Their SAGE Research Methods Online and Cases database includes contents from books, articles, encyclopedias, handbooks, and videos covering social science research design and methods including the complete Little Green Book Series of Quantitative Applications in the Social Sciences and the Little Blue Book Series of Qualitative Research techniques. The database also includes case studies outlining the research methods used in real research projects. This is an excellent source for finding definitions of key terms and descriptions of research design and practice, techniques of data gathering, analysis, and reporting, and information about theories of research [e.g., grounded theory]. The database covers both qualitative and quantitative research methods as well as mixed methods approaches to conducting research.

SAGE Research Methods Online and Cases

• << Previous: Qualitative Methods
• Next: Insiderness >>
• Last Updated: May 2, 2024 4:39 PM
• URL: https://libguides.usc.edu/writingguide

Browse Course Material

Course info.

• Prof. Laurent Demanet

Departments

• Mathematics

As Taught In

• Applied Mathematics
• Computation

Learning Resource Types

Introduction to numerical analysis, course description.

You are leaving MIT OpenCourseWare