Date of Award
August 2015
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Bruce Wade
Second Advisor
Chao Zhu
Committee Members
Richard Stockbridge, Hans Volkmer, Wei Wei
Keywords
Mean-Square Stability, Numerical Solution of Stochastic Differential Equations
Abstract
This work proposes a novel weak Simpson method for numerical solution for a class of stochastic differential equations. We show that such a method has weak convergence of order one in general and weak convergence of order three under certain additional assumptions. This work also aims to determine the mean-square stability region of the weak Simpson method for linear stochastic differential equations with multiplicative noises. In this work, a mean-square stability region of the weak Simpson scheme is identified, and stepsizes for the numerical method where errors propagation are under control in well-defined sense are given. The main results are illustrated with numerical examples.
Recommended Citation
Adhikari, Ram Sharan, "A Weak Simpson Method for a Class of Stochastic Differential Equations and Numerical Stability Results" (2015). Theses and Dissertations. 986.
https://dc.uwm.edu/etd/986