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2014•Journal of Interpolation and Approximation in Scientific ComputingOpen access

Application of the homotopy perturbation method and the homotopy analysis method for the dynamics of tobacco use and relapse

Anant Kant Shukla, Héctor Vázquez-Leal, T. R. Ramamohan, Luis Hernández-Martínez, S. Srinivas, J. Huerta-Chua

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Abstract

We obtain approximate analytical solutions of two mathematical models of the dynamics of tobacco use and relapse including peer pressure using the homotopy perturbation method (HPM) and the homotopy analysis method (HAM). To enlarge the domain of convergence we apply the Padé approximation to the HPM and HAM series solutions. We show graphically that the results obtained by both methods are very accurate in comparison with the numerical solution for a period of 30 years.

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We obtain approximate analytical solutions of two mathematical models of the dynamics of tobacco use and relapse including peer pressure using the homotopy perturbation method (HPM) and the homotopy analysis method (HAM). To enlarge the domain of convergence we apply the Padé approximation to the HPM and HAM series solutions. We show graphically that the results obtained by both methods are very accurate in comparison with the numerical solution for a period of 30 years.

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Available abstract

We obtain approximate analytical solutions of two mathematical models of the dynamics of tobacco use and relapse including peer pressure using the homotopy perturbation method (HPM) and the homotopy analysis method (HAM). To enlarge the domain of convergence we apply the Padé approximation to the HPM and HAM series solutions. We show graphically that the results obtained by both methods are very accurate in comparison with the numerical solution for a period of 30 years.

Key concepts: Homotopy perturbation method, Homotopy analysis method, Homotopy, Perturbation (astronomy), Mathematics, Applied mathematics, Computer science, Biological system

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