On the Solution of Block Tridiagonal Systems of Linear Algebraic Equations Having a Special Structure

Abstract

Recently the present author has developed some high-order finite difference formulae for the approximate numerical integration of general two-point boundary value problems for ordinary differential equations. The algebraic equations arising from using these formulae in conjunction with a modified Newton iteration scheme are block tridiagonal with an additional special structure. Efficient algorithms for solving these equations are given and these appear to make high order finite difference schemes particularly attractive for the numerical solution of general two-point boundary value problems.