<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper, we first propose numerical solution methods for stochastic ordinary differential equations by using the two-step Maruyama method and Euler-Maruyama method in variable substitution, and analyze the mean-square compatibility, mean-square convergence and mean-square linear stability of the corresponding numerical methods, respectively. Finally, 10,000 times value experiments are conducted to verify the convergence accuracy and stability of the variable substitution methods. The results show that the Euler method simulates this equation when taking steps <italic>h</italic> = 0.05, <italic>β</italic> = 5 and <italic>σ</italic> = 2  for numerical experiments, and the numerical results obtained are convergent but unstable. On the other hand, the Euler-Maruyama method with variable substitution is consistent with the real solution. It shows that variable substitution is an important method for solving stochastic ordinary differential equations with high convergence and stability, which is of great significance for the solution of stochastic ordinary differential equations.</p>
</abstract>

In this paper, we first propose numerical solution methods for stochastic ordinary differential equations by using the two-step Maruyama method and Euler-Maruyama method in variable substitution, and analyze the mean-square compatibility, mean-square convergence and mean-square linear stability of the corresponding numerical methods, respectively. Finally, 10,000 times value experiments are conducted to verify the convergence accuracy and stability of the variable substitution methods. The results show that the Euler method simulates this equation when taking steps h = 0.05, β = 5 and σ = 2  for numerical experiments, and the numerical results obtained are convergent but unstable. On the other hand, the Euler-Maruyama method with variable substitution is consistent with the real solution. It shows that variable substitution is an important method for solving stochastic ordinary differential equations with high convergence and stability, which is of great significance for the solution of stochastic ordinary differential equations.

Variable substitution methods in the solution of stochastic ordinary differential equations and their applications

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In this paper, we first propose numerical solution methods for stochastic ordinary differential equations by using the two-step Maruyama method and...

Variable substitution methods in the solution of stochastic ordinary differential equations and their applications

Published Online: Nov 11, 2023

Page range: -

Received: Jan 23, 2023

Accepted: May 22, 2023

DOI: https://doi.org/10.2478/amns.2023.2.01097

Keywords
Stochastic ordinary differential equations, Euler-Maruyama, Numerical solution, Variable substitution, Convergence accuracy

© 2023 Ting Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Variable substitution methods in the solution of stochastic ordinary differential equations and their applications

Published Online: Nov 11, 2023

Page range: -

Received: Jan 23, 2023

Accepted: May 22, 2023

DOI: https://doi.org/10.2478/amns.2023.2.01097

KeywordsStochastic ordinary differential equations, Euler-Maruyama, Numerical solution, Variable substitution, Convergence accuracy

© 2023 Ting Zhang, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Stochastic ordinary differential equations, Euler-Maruyama, Numerical solution, Variable substitution, Convergence accuracy