Solution of partially singularly perturbed system of initial and boundary value problems using non-uniform Haar Wavelet

Abstract

An efficient non-uniform Haar wavelet method is proposed for the numerical solution of system of first order linear partially singularly perturbed initial value problem on piecewise uniform Shishkin mesh and ρ-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 finite difference operator method and parameter uniform methods. We demonstrated two test problems to support the theory, accuracy and efficiency of the non-uniform Haar Wavelet method.