Nonpolynomial spline finite difference scheme for nonlinear singuiar boundary value problems with singular perturbation and its mechanization

Pages: 355 - 363, Issue special, November 2013

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Navnit Jha - Department of Mathematics, South Asian University, Akbar Bhawan, Chanakyapuri, New Delhi-110021, India (email)

Abstract: A general scheme for the numerical solution of nonlinear singular perturbation problems using nonpolynomial spline basis is proposed in the paper. The special non-equidistant formulation of mesh takes into account the boundary and interior layer structures. The proposed scheme is almost fourth order accurate and applicable to both singular and nonsingular cases. Convergence analysis of the scheme is briefly discussed. Maple program for the generation of difference scheme is presented. Computational illustrations characterized by boundary and interior layers show that the practical order of accuracy is close to the theoretical order of the method.

Keywords:  Singular perurbation, reaction-convection-diffusion, finite difference, nonpolynomial splines, compact operator.
Mathematics Subject Classification:  Primary: 65L10, 65L12; Secondary: 34B16.

Received: September 2012; Published: November 2013.