An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method

Abstract

A rapid and effective way of working out the optimum convergence control parameter in the homotopy

analysis method (HAM) is introduced in this paper. As compared with the already known

ways of evaluating the convergence control parameter in HAM either through the classical constant

h

−

curves (h

is the convergence control parameter) or from the classical squared residual error as

frequently used in the literature, a novel description is proposed to find out an optimal value for the

convergence control parameter yielding the same optimum values. In most cases, the new method

is shown to perform quicker and better against the residual error method when integrations are

much harder to evaluate. Examples involving solution of algebraic, highly nonlinear differentialdifference,

integro-differential, and ordinary or partial differential equations or systems, all from

the literature demonstrate the validity and usefulness of the introduced technique