Spline wavelets in numerical resolution of partial differential equations

Abstract

We give a review of applications of spline wavelets in the resolution of partial differential equations. Two typical methods for numerical solutions of partial differential equations are Galerkin method and collocation method. Corresponding to these two methods, we present the constructions of semi-orthogonal spline wavelets and semiinterpolation spline wavelets respectively. We also show how to use them in the numerical resolution of various partial differential equations.