Multiresolution Solution of Burgers Equation with B-spline Wavelet Basis

Abstract

This paper represents a mixed numerical method for the multi-resolution solution of non-linear partial differential equations based on B-Spline wavelets. The method is based on a second-order finite difference formula combined with the collocation method which uses the wavelet basis and applied to the Burgers equation. Performance and accuracy of the numerical solutions are studied using three standard test cases with Dirichlet and Neumann boundary conditions. Comparing the results with other methods such as the fully implicit finite difference method and mixed finite difference/boundary element method shows a greater accuracy while using the smaller number of basis functions.