A Weak Simpson Method for a Class of Stochastic Differential Equations and Numerical Stability Results

File(s)
Date
2015-08-01Author
Adhikari, Ram Sharan
Department
Mathematics
Advisor(s)
Bruce Wade
Chao Zhu
Metadata
Show full item recordAbstract
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.
Subject
Mean-Square Stability
Numerical Solution of Stochastic Differential Equations
Permanent Link
http://digital.library.wisc.edu/1793/94409Type
dissertation