Solution of variational problems via hybrid of block-pulse and lagrange interpolating

A direct method for solving variational problems using the hybrid of block-pulse functions and Lagrange interpolating polynomials is presented. The method is based upon hybrid functions approximations. The properties of hybrid functions, which consist of block-pulse functions and Lagrange interpolating polynomials, are presented. These properties are then utilised to reduce the variational problems to the solution of non-linear equations. Three examples are considered, in the first example the classical brachistochrone problem is studied and in the second and third examples, two non-linear problems are examined. The method is general, easy to implement and yields very accurate results.