An effective homotopy analysis method to solve the cubic isothermal auto-catalytic chemical system

K. M. Saad; O. S. Iyiola; P. Agarwal; K. M. Saad; O. S. Iyiola; P. Agarwal

doi:10.3934/Math.2018.1.183

AIMS Mathematics

2018, Volume 3, Issue 1: 183-194. doi: 10.3934/Math.2018.1.183

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Research article

An effective homotopy analysis method to solve the cubic isothermal auto-catalytic chemical system

1.
Department of Mathematics, Faculty of Arts and Sciences, Najran, Najran University, Saudi Arabia
2.
Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen
3.
Department of Mathematical Sciences, Minnesota State University Moorhead, MN USA
4.
Department of Mathematical, Anand International College of Engineering, Jaipur-303012, India
5.
Center for Basic and Applied Sciences, Jaipur-302029, India

Received: 17 September 2017 Accepted: 31 January 2018 Published: 21 March 2018

We established an effective algorithm for the homotopy analysis method (HAM) to solve a cubic isothermal auto-catalytic chemical system (CIACS). Our solution comes in a rapidly convergent series where the intervals of convergence given by h-curves and to find the optimal values of h, we used the averaged residual errors. The HAM solutions are compared with the solutions obtained by Mathematica in-built numerical solver. We also show the behavior of the HAM solution.
- isothermal auto-catalytic,
- chemical system,
- homotopy analysis method,
- averaged residualerrors
Citation: K. M. Saad, O. S. Iyiola, P. Agarwal. An effective homotopy analysis method to solve the cubic isothermal auto-catalytic chemical system[J]. AIMS Mathematics, 2018, 3(1): 183-194. doi: 10.3934/Math.2018.1.183

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Abstract

We established an effective algorithm for the homotopy analysis method (HAM) to solve a cubic isothermal auto-catalytic chemical system (CIACS). Our solution comes in a rapidly convergent series where the intervals of convergence given by h-curves and to find the optimal values of h, we used the averaged residual errors. The HAM solutions are compared with the solutions obtained by Mathematica in-built numerical solver. We also show the behavior of the HAM solution.

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