Date of Award
Doctor of Philosophy
Richard Stockbridge, Hans Volkmer, Wei Wei
Mean-Square Stability, Numerical Solution of Stochastic Differential Equations
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.
Adhikari, Ram Sharan, "A Weak Simpson Method for a Class of Stochastic Differential Equations and Numerical Stability Results" (2015). Theses and Dissertations. 986.