### Numerical Solution of Boundary Layer Problem Using Second Order Variable Mesh Method

D. Swarnakar, B. S. L. Soujanya G.

#### Abstract

In this paper, a second-order finite difference method on non-uniform grid is proposed for the solution of singularly perturbed boundary value problems. Replace the derivatives of the problem with highorder finite differences on a non-uniform grid to get a discrete equation. This equation can be effectively solved by tridiagonal method. This method performs convergence analysis and the method produces second-order consistent convergence. The numerical experiments are used to illustrate the method. The absolute error has been proposed to compare with other methods in the literature to prove the rationality of the method.

#### Keywords

Non-uniform grid; Finite difference method; Singularly perturbed boundary value problem; Boundary layer

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DOI: http://dx.doi.org/10.26713%2Fcma.v11i3.1350

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