Sur les ondelettes de legendre pour l’equation de poisson dans le cadre d’une solution complexe

Abstract

On Legendre wavelets for Poisson equation in the frame of a complex solution. In this work, we presented a numerical method for solving different types of differential equations (ordinary differential equations, partial differential equations, and fractional differential equations) called the "Legendre wavelet method". This method transforms a differential equation into a system of algebraic equations using so-called operational matrices of integration and derivation. After solving this system, we obtain solutions that are as approximate as desired for the given equation. We were able to apply this method to the two-dimensional Poisson equation in the set of complex numbers ℂ, using for the first time both operational matrices at the same time, which made this method faster and more accurate.