Numerical Solution of Elliptic Boundary Value Problems by Spline Functions

Abstract

A numerical method for solving linear, two-dimensional elliptic boundary value problems is presented. The method is essentially the Ritz procedure which uses; polynomial spline functions to approximate the exact solution. The spline functions are constructed by defining a polynomial function over each of a set of disjoint subdomains and imposing certain compatibility conditions along common boundaries between subdomains. The main advantage of the methods is that it does not even require the continuity of the spline functions across the boundaries between subdomains. Therefore it is easy to construct classes of spline functions which will produce any specified rate of convergence.