Haar wavelet collocation method for three-dimensional elliptic partial differential equations

Abstract

A new collocation method based on Haar wavelet is presented for numerical solution of three-dimensional elliptic partial differential equations with Dirichlet boundary conditions. An important advantage of the method is that it can be applied to both linear as well as nonlinear problems. The algorithm based on this new method is simple and can be easily implemented in any programming language. Experimental rates of convergence of the proposed method are calculated which are in agreement with theoretical results. The proposed method is applied to several benchmark problems from the literature including linear and nonlinear elliptic problems as well as systems of elliptic partial differential equations. The numerical experiments confirm the accuracy and diverse applicability of the method.