Moving least squares and spectral collocation method to approximate the solution of stochastic Volterra-Fredholm integral equations

摘要

In this article, an idea based on moving least squares (MLS) and spectral collocation method is used to estimate the solution of nonlinear stochastic Volterra-Fredholm integral equations (NSVFIEs). The main advantage of the suggested approach is that in some parts where interpolation and integration are necessary, this approach does not require any meshes. Therefore, it is independent of the geometry of the domains, and this advantage helps us to solve the problems on irregular domains with relatively fewer computations. Another advantage of our proposed method is that with a small number of points and base functions, we were able to obtain the results with acceptable accuracy, and this is very attractive and practical. Applying the proposed method leads to the conversion of the problem into a system of algebraic equations. It is worth noting, some examples and error estimations have been provided to illustrate the accuracy and applicability of this technique. Also, we present a convergence analysis of the proposed method.