Wavelet collocation method based on Legendre polynomials and its application in solving the stochastic fractional integro-differential equations

This work is an extended version of the ICCS 2020 conference paper [1]. The paper aims to present an efficient numerical method to quantify the uncertainty in the solution of stochastic fractional integro-differential equations. The numerical method presented here is a wavelet collocation method based on Legendre polynomials, and their deterministic and stochastic operational matrix of integration. The operational matrices are used to convert the stochastic fractional integro-differential equation to a linear system of algebraic equations. The accuracy and efficiency of the proposed method are validated through numerical experiments. Moreover, the results are compared with the numerical methods based on the Gaussian radial basis function (GA RBF) and thin plate splines radial basis function (TBS RBF) to show the superiority of the proposed method. Finally, concerning the real-world application, a stock market model has been simulated and the results are demonstrated.

Automated summary

This paper presents an efficient numerical method to quantify uncertainty in solving stochastic fractional integro-differential equations, converting them into algebraic equation systems using wavelet collocation method and Legendre polynomials. The proposed method is validated for accuracy and efficiency through numerical experiments, showing superiority over Gaussian and thin plate splines radial basis function methods. Additionally, a stock market model is simulated and results are demonstrated for real-world application.