## Quadratic spline solution of Calculus of Variation Problems

## Quadratic spline solution of Calculus of Variation Problems

*R. Mohammadi, A. S. Alavi*

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## Abstract

In this paper, we developed numerical method of order O(h2) 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 nite dierence methods. Convergence analysis and a bound on the approximate solution are discussed. Numerical examples are also given to demonstrate the higher accuracy and eciency of our method.

## Keywords

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