Method of Lines With Haar Wavelet For Solving Parabolic Differential Equation

In this paper we present a theoretical framework and numerical comparisons for a wavelet-based algorithm associated with both method of lines and wavelets for solving some partial differential equations. In particular, we consider a wavelet-based algorithm using Method of Lines (MOL) analysis. The advantage is in the simplicity of the boundary modification, and relatively simple and small representing the differential operators, in contrast to other wavelet-based algorithms. The time of calculations and number of flops were reduced using Haar wavelets, and as a demonstration, an example for solving the diffusion equation.<br /> Key words: Method of Lines, partial differential equations, Haar wavelet