A NUMERICAL TECHNIQUE FOR SOLVING A CLASS OF VARIATIONALPROBLEMS WITH SUITABLE BOUNDARY CONDITIONS

An effective numerical method based upon Legendre polynomials is proposed for the solution of a class ofvariational problems with boundary conditions. The Ritz spectral method is used for finding the approximatesolution of the problem. By utilizing the Ritz method, the given nonlinear variational problem reduces tothe problem of solving a system of algebraic equations. The advantage of the Ritz method is that itprovides greater flexibility in which the boundary conditions are imposed at the end points of the interval.Furthermore, compared with the exact solution of the problem, the satisfactory results obtained with lowterms of basis. An illustrative example is included to demonstrate the validity and applicability of theproposed technique.