An Exponential Spline Difference Scheme for Solving a Class of Boundary Value Problems of Second-Order Ordinary Differential Equations

Abstract

In this paper, we mainly study an exponential spline function space, construct a basis with local supports, and present the relationship between the function value and the first and the second derivative at the nodes. Using these relations, we construct an exponential spline-based difference scheme for solving a class of boundary value problems of second-order ordinary differential equations (ODEs) and analyze the error and the convergence of this method. The results show that the algorithm is high accurate and conditionally convergent, and an accuracy of 1/240h6 was achieved with smooth functions.