Approximate Solution of Second Order Singular Perturbed and Obstacle Boundary Value Problems Using Meshless Method Based on Radial Basis Functions

Abstract

AbstractIn this article, a meshless numerical technique based on radial basis functions (RBFs) is proposed for the solution of singular perturbed, obstacle, and second-order boundary value problems. First, the unknown function and their derivatives are approximated by RBFs which reduces the given problem into a system of algebraic equations which is easy to solve. The shape parameter involved in RBFs is chosen by the hit and trial method. Despite this, the convergence of the scheme is briefly discussed numerically. The nonlinear terms are linearized by quasi-linearization technique. The main objective of this paper is to show that the meshless RBFs-based method is convenient for various classes of boundary value problems. Efficiency and performance of the proposed technique are examined by calculating absolute error norms. Obtained accurate results confirm applicability and efficiency of the method.