An efficient numerical algorithm for multi-dimensional time dependent partial differential equations

Abstract

An efficient and robust numerical scheme based on Haar wavelets and finite differences is suggested for the solution of two-dimensional time dependent linear and nonlinear partial differential equations (PDEs). Excellent feature of the scheme is the conversion of linear and non-linear PDEs to algebraic equations which are comparatively easy to handle. Convergence of the scheme, which guarantees small error norm as the resolution level increases, is also an important part of this work. Different error norms are computed to check efficiency of the technique. Computations verify accuracy, flexibility and low computational cost of the method.