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

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

Developing Clean Technology through Approximate Solutions of Mathematical Models

In this paper, the role of mathematical modeling in the development of clean technology has been considered. One method each for obtaining approximate solutions of mathematical models by ordinary differential equations and partial differential equations respectively arising from the modeling of systems and physical phenomena has been considered. The construction of continuous hybrid methods for the numerical approximation of the solutions of initial value problems of ordinary differential equations as well as homotopy analysis method, an approximate analytical method, for the solution of nonlinear partial differential equations are discussed