A Hybrid Method for Singularly Perturbed Convection–Diffusion Equation

Abstract

In this research, we present a hybrid method which combination of simplified reproducing kernel method (SRKM) and asymptotic expansion for solving singularly perturbed convection–diffusion problems. According to the hybrid method, firstly asymptotic expansion formed on boundary layer domain and then terminal value problem solved via SRKM on regular domain. To apply the SRKM, some special Hilbert spaces are defined and related reproducing kernel functions are given. Then, the approximate solution is obtained as serial form. A new algorithm of SRKM is presented for nonlinear problem. Also, convergence analysis of approximate solution is given. Some linear and nonlinear problems are solved by hybrid method. The obtained outcomes indicate that the hybrid method is reliable and very effective for solving singularly perturbed convection–diffusion equation.