ABSTRACT
One of the most important and known mathematical models used to describe nature are partial differential equations (PDEs). This chapter discusses the contribution of wavelet theory and re-develops some wavelet-based methods in the solutions of PDEs. It re-develops some prototypical example of application of wavelets in resolving partial differential equations. Wavelet-Galerkin method permits reduction of the order of derivative in the original problem by transforming the problem into a variation alone. The chapter develops some illustrative experiments to show the feasibility of the wavelet representations as well as their efficient implementations. It discusses the second typical problem in elliptic differential equation, which consists of the Neumann problem.
