A New Method for Solving Nonlinear BVPs

As we know, the homotopy analysis method (HAM) provides us with a convenient way to adjust and control the convergence region and rate of the obtained series solutions. This great advantage of method is possible by finding a proper value of the so-called control parameter . In this paper, an efficient way of obtaining is proposed. Such value of parameter can be determined at the any order of approximation of HAM series solution, by solving of a nonlinear polynomial equation. To show the ability and efficiency of this new approach we apply this modification of HAM to some linear and nonlinear initial value problems, and obtain convergent series solutions which agree very well with their exact solutions. It is found that presented approach greatly accelerate the convergence of series solution.