Hybrid Functions in the Calculus of Variations

Abstract

The solution of problems in the calculus of variations is obtained by using hybrid functions. The properties of the hybrid functions which consist of block-pulse functions plus legendre polynomials and block-pulse functions plus Chebyshev polynomials are presented. Two examples are considered, in the first example the brachistochrone problem is formulated as a nonlinear optimal control problem, and in the second example an application to a heat conduction problem is given. The operational matrix of integration in each case is introduced and is utilized to reduce the calculus of variations problems to the solution of algebraic equations. The method is general, easy to implement and yields very accurate results.