Tension spline method for the solution of elliptic equations

Abstract

In this paper, two classes of methods are developed for the solution of two-dimensional elliptic partial differential equations. We have used tension spline function approximation in both x and y spatial directions and a new scheme of order $O(h^4 + k^4) $ has been obtained. The convergence analysis of the methods has been carried out. Numerical examples are given to illustrate the applicability and accurate nature of our approach.

Keywords

• elliptic partial differential equation
• tension spline function
• iterative method
• convergence analysis