Indirect Algorithm for Solving Variation Problems

Abstract

     In this work, an approximate indirect method to solve some variational problems is proposed in terms of shifted Legendre polynomials. The operational matrix of differentiation for shifted Legendre polynomials is first derived. Using the operational matrix of differentiation, the variational problems are reduced to the solution of system of algebric equations with unknown shifted Legendre coefficients. Numerical example illustrates the efficiency, simplicity and accuracy of the proposed method.