Boundary layer challenges: A comparative analysis of two efficient meshless approaches

This article presents two meshless computational techniques: the radial basis function (RBF) method and the polynomial method, for numerically analyzing boundary layer problems, with a specific focus on singularly perturbed two-point boundary value problems. Both of these suggested meshless methods offer an advantage over globally supported meshless techniques, as they involve approximating derivatives by employing a constrained set of nodes located in the neighborhood of each collocation node. As a result, they demand significantly reduced computational effort compared to the globally supported collocation method. To assess the accuracy of these methods, we employ the maximum error norm, and the results are presented in the form of tables and graphs. The simulation results demonstrate that both approaches exhibit robust performance in addressing the investigated boundary layer problems.