SOLUTION OF PARTIALLY SINGULARLY PERTURBED SYSTEM OF INITIAL AND BOUNDARY VALUE PROBLEMS USING NON-UNIFORM HAAR WAVELET

SOLUTION OF PARTIALLY SINGULARLY PERTURBED SYSTEM OF INITIAL AND BOUNDARY VALUE PROBLEMS USING NON-UNIFORM HAAR WAVELET

A. Raza, A. Khan, K. Ahmad

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Abstract

An ecient non-uniform Haar wavelet method is proposed for the numerical solution of system of rst order linear partially singularly perturbed initial value prob- lem on piecewise uniform Shishkin mesh and -mesh. Further, we apply same technique for solving system of second order linear partially singularly perturbed boundary value problems on piecewise uniform Shishkin mesh and q-mesh. Our method produces better results in comparison to uniform Haar wavelet, classical nite dierence operator method and parameter uniform methods. We demonstrated two test problems to support the theory, accuracy and eciency of the non-uniform Haar Wavelet method.

Keywords

System of Dierential Equations; Non-Uniform HaarWavelet; Shishkin Mesh; Singular Perturbation; Initial and Boundary Value Problems.