BERNSTEIN DIRECT METHOD FOR SOLVING VARIATIONAL PROBLEMS

Abstract

A simple algorithm for solving variational problems via Bernstein orthonormal polynomials of degree six is proposed. The sixth order Bernstein polynomials are orthonormalized and their operational matrix of integration is derived. Using this operational matrix of integration, the variational problems are reduced to the solution of systems of algebraic equations. The method of Lagrange multipliers is used to solve illustrative problems with free and constrained boundaries. Mathematics Subject Classification: 65K10, 49J99