An algorithm of the boundary value problem based on multiscale orthogonal compact base

Abstract

The basis scope of this paper is to introduce a set of orthonormal basis functions and to present a new algorithm for solving the boundary value problem by defining the ε-approximate solution, where the ε-approximate solution is defined in this article. First, the basis functions are introduced and proved to be orthonormal. Second, the ε-approximate solution is defined and proved to be the optimal solution. Third, the algorithm is proposed and proved to be stable and uniformly convergent. Finally, numerical examples are presented to confirm the theoretical results and show that the proposed method has wide application foreground.