Contributed Papers

Journal of Optimization Theory and Applications

, Volume 76, Issue 3, pp 415-428

First online:

Cubic spline method for a class of nonlinear singularly-perturbed boundary-value problems

  • M. K. KadalbajooAffiliated withDepartment of Mathematics, Indian Institute of Technology
  • , R. K. BawaAffiliated withDepartment of Mathematics, Indian Institute of Technology

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Abstract

In this paper, we present a numerical method for solving a class of nonlinear, singularly perturbed two-point boundary-value problems with a boundary layer on the left end of the underlying interval. The original second-order problem is reduced to an asymptotically equivalent first-order problem and is solved by a numerical method using a fourth-order cubic spline in the inner region. The method has been analyzed for convergence and is shown to yield anO(h 4) approximation to the solution. Some test examples have been solved to demonstrate the efficiency of the method.

Key Words

Singularly-perturbed boundary-value problems boundary layers cubic splines singularly-perturbed initial-value problems nonasymptotic methods