A fast numerical method for solving calculus of variation problems

In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years, differential transform method has been attracted a lot of attention of the researchers for solving nonlinear problems. This method finds the solution of the problem without any discretization of the equation. Since this method gives a closed form solution of the problem and avoids the round off errors, it can be considered as an efficient method for solving various kinds of problems. In this research, differential transform method (DTM) will be employed for solving some problems in calculus of variations. Some examples are presented to show the efficiency of the proposed technique.