Quadratic spline solution of Calculus of Variation Problems

Year 2015, Volume: 5 Issue: 2, 276 - 285, 01.12.2015

R. Mohammadi A. S. Alavi

Abstract

In this paper, we developed numerical method of order O h 2 and based on quadratic polynomial spline function for the numerical solution of class of two point boundary value problems arising in Calculus of Variation. The present approach gives better approximations over all the existing finite difference methods. Convergence analysis and a bound on the approximate solution are discussed. Numerical examples are also given to demonstrate the higher accuracy and efficiency of our method.

Keywords

Calculus of variation, Euler-Lagrange equation, quadratic polynomial spline, Convergence

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• Reza Mohammadi is an Assistant Professor of Applied Mathematics in School of Basic Sciences, University of Neyshabur, Neyshabur, Iran, since