Numerical Solution of Two-Parameter Singularly Perturbed Convection-Diffusion Boundary Value Problems via Fourth Order Compact Finite Difference Method

Abstract

In this study, we have developed a fourth order compact finite difference method for finding the numerical solution of two-parameter singularly perturbed convection-diffusion boundary value problems. We have used fourth order compact finite difference method on uniform mesh which provides a tridiagonal linear system of equations. The convergence analysis of the proposed method is established through a matrix analysis approach and it is proved that present method gives fourth order convergence results. Present method is implemented on two numerical examples for checking the efficiency and precision of the method. Numerical outcomes are exhibited which supports the theoretical outcomes. Numerical outcomes are compared with other existing methods and found that present method gives more accurate approximate solution as compare to the other existing methods.