A numerical approach to solve the stochastic Allen-Cahn equation of fractional order

In this paper, we employ a collocation method based on Legendre polynomials (LPs) to solve the time-fractional stochastic Allen-Cahn equation. This method is applied to convert the solution of this stochastic equation to the solution of a nonlinear system of algebraic equations. The numerical approach is completely described. Finally, a test example is implemented to validate the robustness of the proposed scheme.

کلیدواژه ها:

Stochastic Allen-Cahn equation ، Caputo's derivative ، Legendre polynomials ، Collocation scheme