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 dif-ferential equations are Galerkin method and collocation method. Corresponding to these two methods, we present the constructions of semi-orthogonal spline wavelets and semi-interpolation spline wavelets respectively. We also show how to use them in the numerical resolution of various partial differential equations.