A New Technique of The q-Homotopy Analysis Method for Solving Non-Linear Initial Value Problems

Shaheed N. Huseen; Nada M. Ayay

Shaheed N. Huseen University of Thi-Qar, Faculty of Computer Science and Mathematics,Mathematics Department, Thi-Qar, Iraq
Nada M. Ayay University of Thi-Qar, Faculty of Education for Pure Science, Mathematics Department, Thi-Qar, Iraq

Keywords: q-Homotopy analysis technique, Initial value problem, Convergence control parameter.

Abstract

In this paper, a new procedure of the q-homotopy analysis technique (NTqHAM) was submitted for solving non-linear initial value problems. The NTq-HAM contains just a single convergence control parameter α. To show the dependability and proficiency of the technique, this approach is applied to solve two non-linear IVPs, and the outcomes uncover that the NTq-HAM is more general of the He’s homotopy perturbation technique (HPM) [27] and the He’s HPM is only special case of the NTq-HAM when α = 1.

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