numerical methods phd thesis

efficient numerical methods to simulate those SDEs is an important research topic. The goal of this thesis is to introduce the recent development of those numerical methods, including our own work on the weak convergence of the Euler-Maruyama

Numerical methods to solve initial value problems of differential equations progressed quite a bit in the last century. We give a brief summary of how useful numerical methods are for ordinary differential equations of first and higher order. In this thesis both computational and theoretical discussion of the application of numerical methods on differential equations takes place. The thesis ...

The goal of this thesis is to develop methods for the efficient numerical solution of such equations that are also robust for nonsmooth potentials and anisotropic surface energies. These methods are derived for the Cahn-Hilliard equation that are prototypic for a multitude of such models.

Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid. PhD Theses 2022. Author. Title. James Petrie. Decentralized contact tracing protocols and a risk analysis approach to pandemic control. Yiming Meng. Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties.

on can consider probabilistic numerical methods, which output a probability distribution over the quantity of interest. In recent years, this idea has emerged into a new field of research, called Probabilistic Numerics. In the first part of this thesis, an exact Bayesian probabilistic numerical method for or-

NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS WITH APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS A thesis submitted for the degree of Doctor of Philosophy by Abdul Qayyum Masud Khaliq Department of Mathematics and Statistics, Brunel University Uxbridge, Middlesex, England. UB8 3PH

PhD Thesis Numerical Methods for Nonlinear PDEs in Finance Author: Sima Mashayekhi This thesis submitted in ful lment of the requirements for the degree of Doctor of Philosophy ... PhD thesis submitted to the PhD School of Science, Faculty of Science, University of Copen-hagen, Denmark, in September 2015.

T.H.A. Frame - Methods of targeting observations for the improvement of weather forecast skill. 2005. C. Hughes - On the topographical scattering and near-trapping of water waves. B.V. Wells - A moving mesh finite element method for the numerical solution of partial differential equations and systems

In this PhD thesis, we construct numerical methods to solve problems described by advectiondiffusion and convective Cahn-Hilliard equations. The advection-diffusion equation models a variety of physical phenomena in fluid dynamics, heat transfer and mass transfer or alternatively describing a stochastically-changing system.

the general approach 'the method of lines' [84] to stiff timedependent PDEs. In this method we first discretize the spatial derivatives of a PDE with a spatial derivative approximation method, which results in a stiff coupled system of ordinary differential equations (ODEs) in time only. Then, we apply any well established numerical

This dissertation concerns the numerical approximations of solutions of fully nonlinear second order partial differential equations (PDEs). The numerical methods and analysis are based on a new concept of weak solutions called moment solutions, which unlike viscosity solutions, are defined by a constructive method called the vanishing moment method. The main idea of the vanishing moment method ...

Since the efficient application of the developed method often requires nontrivial numerical software, we also work on the design and development of numerical software libraries with a special focus on flexible and clean interfaces without sacrificing efficiency. For more information see Projects and PhD Theses.

Numerical Iterative Methods For Nonlinear Problems Author: Malik Zaka Ullah Supervisor: Prof. Stefano Serra-Capizzano Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the program Mathematics of Computing: Models, Structures, Algorithms, and Applications June 2015

The goal of this PhD project is to develop robust, high-order accurate numer-ical methods for predicting the interaction between nonlinear ocean waves and marine structures. This will serve as a rst step for developing a highly e -cient solver for the seakeeping and added resistance of ships in short waves. A

The systematic study of numerical methods for singular perturbation problems started somewhat later in the 1970s. From this time onwards the research frontier has steadily ex-panded, but the exposition of new developments in the analysis of these numerical methods has not received its due attention.

A. Scascighini, A numerical method for the design of internal flow configurations based on the inverse Euler equations (2001) PhD Thesis, ETH Diss Nr. 14440, Examiner Prof. Dr. Rolf Jeltsch DOI call_made BibTeX

nonsmooth, rigid body dynamics," Computer Methods in Applied Mechanics and Engineering, vol. 200, no. 5-8, pp. 439-453, 2011. [2] T. Heyn, On the Modeling, Simulation, and Visualization of Many-Body Dynamics Problems with Friction and Contact. PhD thesis, Department of Mechanical Engineering, University of Wisconsin-Madison,

This thesis is dedicated to developing numerical methods to solve fluid-structure interaction (FSI) problems. FSI features in a vast range of physical systems and has a wide application in engineering. In the first chapter of this document we provide a literature review on different numerical methods for FSI problems. The work of

Numerical Optimization Methods on Riemannian Manifolds. This dissertation considers the generalization of two well-known unconstrained optimization algorithms for Rn to solve optimization problems whose constraints can be characterized as a Riemannian manifold. Efficiency and effectiveness are obtained compared to more traditional approaches to ...

In this thesis, we use the variational iteration technique and its various modifications to suggest and analyze several iterative methods for finding the approximate solution of the nonlinear equations. Using suitable finite difference schemes, a number of new iterative methods free from second derivative are considered and analyzed.

Fees. Fees for entry in 2025 have not yet been set. For reference, the fees for the academic year beginning September 2024 were as follows: PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500. International, including EU, students (per annum): Band A £28,000; Band B £ ...

This thesis first tries to study the numerical properties of the master equation using existing numerical methods and parallel machines. Next, approximation algorithms, namely the adaptive aggregation method and the radial basis function collocation method, are proposed as new paths to resolve the "curse of dimensionality".

More precisely, we develop in two dimensional domain novel numerical methods called fitted Multi-Point Flux Approximation (MPFA) methods to solve the multi-dimensional Black-Scholes PDE for pricing American and European options. We investigate two types of MPFA methods, the O-method which is the classical MPFA method and the most intuitive ...