Numerical Mean-square and Asymptotic Stability Analysis for the Weak Simpson Method

Authors

  • Ram Sharan Adhikari Faculty of mathematics, Rogers State University, Claremore, OK, 7401, USA

DOI:

https://doi.org/10.3126/ijorn.v11i1.64694

Keywords:

Stochastic differential equation, Numerical method, Euler-Maruyama method, Mean-square stability, Asymptotic stability, Weak convergence

Abstract

A weak Simpson method has order of weak convergence one in general and has order of weak convergence three under certain additional assumptions. The proposed method has the potential to overcome some of the numerical instabilities that are often experienced when using explicit Euler methods. This work 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 step-sizes for the numerical method where errors propagation are under control in a well-defined sense are given. The main results are illustrated with numerical examples.

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Published

2023-12-31

How to Cite

Adhikari, R. S. (2023). Numerical Mean-square and Asymptotic Stability Analysis for the Weak Simpson Method. International Journal of Operational Research/Nepal, 11(1), 15–24. https://doi.org/10.3126/ijorn.v11i1.64694

Issue

Vol. 11 No. 1 (2023)

Section

Articles

License

Copyright (c) 2023 International Journal of Operational Research/Nepal

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