Numerical solution of singularly perturbed 2D parabolic initial‐boundary‐value problems based on reproducing kernel theory: Error and stability analysis

Abstract

AbstractThe main aim of this article is to propose two computational approaches on the basis of the reproducing kernel Hilbert space method for solving singularly perturbed 2D parabolic initial‐boundary‐value problems. For each approach, the solution in reproducing kernel Hilbert space is constructed with series form, and the approximate solution um is given as an m‐term summation. Furthermore, convergence of the proposed approaches is presented which provides the theoretical basis of these approaches. Finally, some numerical experiments are considered to demonstrate the efficiency and applicability of proposed approaches.