A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems

Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject certain conditions. This article introduces a novel approach for solving BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation is employed, enabling learning from training data enhancing accuracy. The consist of given exact distances between exterior fictitious sources points, which construct RBFs, such as multiquadric inverse RBFs. distinctive feature it avoids discretization governing equation BVPs. Consequently, proposed ANN-based RBF method offers simplicity with only To validate model, applied solve two- three-dimensional results study highlight effectiveness efficiency method, demonstrating its capability deliver accurate minimal input while relying solely on