Investigation on Ginzburg-Landau equation via a tested approach to benchmark stochastic Davis-Skodje system

Abstract

We propose new numerical methods with adding a modified ordinary differential equation solver to the Milstein methods for solution of stiff stochastic systems. We study a general form of stochastic differential equations so that the Ginzburg-Landau equation and the Davis-Skodje model can be considered as special states of them. The efficiency of the method is experimented, in terms of the convergence rate and accuracy of approximate solution, employing some numerical examples, including stochastic Ginzburg-Landau equation and a paradigm of chemical reaction systems.

Keywords

• Stochastic differential equations
• Chemical reaction systems
• Milstein method
• Convergence rate