An Improvement Meshless Method for the Numerical Solution of Two-Dimensional Stochastic Fredholm Integral Equations

In this paper, a new adaptive meshless scheme based on the regularized moving least squares approximation combined with Ito^ approximation is employed to solve two-dimensional stochastic integral equations. This approach is proposed for handling a singular moment matrix in the context of meshfree methods based on moving least squares approximation. A valuable advantage of applying this technique is that the results converge more quickly to the exact solution by using a small support domain, and it is more flexible because it allows an easy adaptation of the nodal density. The computational complexity is presented to measure the usage time of the proposed approach. The convergence rate of the new method is provided. The numerical test problems are presented and compared with the results obtained by other meshless methods to verify the efficiency and accuracy of the proposed scheme. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.