Direct Restarted Pell Algorithm for Solving Calculus of Variation Problems

Abstract

The Pell Polynomial series is employed to solve problems in calculus of variations. The solution can be considered as linear combinations of Pell polynomials with unknown coefficients. Then a calculus of variational problem transforms into an optimization problem and will be solved using mathematical programming techniques. The proposed method converges rapidly to the exact solution and gives accurate results using small number of Pell polynomials basis polynomials. Some illustrative examples are included and the approximate results obtained by restarted Pell series are compared with the exact solutions.