A variable-mesh approximation method for singularly perturbed boundary-value problems using cubic spline in tension

Abstract

A non-uniform mesh difference scheme using cubic spline in tension is presented to solve a class of non-turning point singularly perturbed two point boundary-value problems for second-order ordinary differential equations with a small parameter multiplying the highest derivative subject to Dirichlet-type boundary conditions. To demonstrate the applicability of the proposed method, two numerical examples have been solved and the results are presented along with their comparison with those obtained with and without variable mesh. This paper is a continuation of the previous work [Aziz, T. and Khan, A. (2002). A spline method for second order singularly-perturbed boundary-value problems. J. Comput. Appl. Math., 147(2), 445–452.] given for uniform mesh case.

Keywords:

• Cubic spline in tension
• Boundary layers
• Variable-mesh difference scheme
• Singular perturbation
• Heat transport problems