Meshless Barycentric Rational Interpolation Method for Solving Nonlinear Stochastic Fractional Integro-Differential Equations

This article suggests an accurate computational approach based on meshless barycentric rational interpolation and spectral method to solve a class of nonlinear stochastic fractional integro-differential equations. These equations have various applications in many aspects of science. The nonlinearity of the equations and the existence of the random factors make their most existing numerical simulations difficult. Therefore, developing an efficient and accurate solver is a challenge. The method introduced in this study converts the given problem into a set of algebraic equations that are nonlinear in nature. Hence, the difficulty of addressing the problem mentioned above is greatly diminished. This article highlights the advantages of meshless barycentric rational interpolation, such as their meshless nature and simplicity of usage in nonlinear problems and the high accuracy of this technique. Due to the random nature of the studied problems, the exact solutions to these problems are not available. Therefore, to ensure the accuracy of the calculated solutions, we provide an error evaluation that can be applied to different problems. We assess the precision of this meshless technique through numerical examples. The simple process of this method clearly reveals its superiority over other available methods. Furthermore, a noteworthy innovation in this research is achieving satisfactory accuracy with a small number of interpolation nodes and basis functions.