The Study of Non-linear Reaction Diffusion System through Homotopy Analysis Method

Hafiz Abdul Wahab, Hazrat Ali, Khalid Usman, Muhammad Naeem, Saira Bhatti, Muhammad Shahzad, Sarfraz Ahmed


In this paper, the homotopy analysis method is applied to the non-linear reaction-diffusion system of Lotka-Volterra type subject of extensive numerical and analytical studies. The comparisons of the other analytical techniques are presented in tables to show the accuracy of this method. The results show that the homotopy analysis method is more reliable than the other available techniques giving the advantage of the choice of some quantities such as initial guess, auxiliary function, an auxiliary parameter that play an important role in the convergence of the series solution.


Alabdullatif,M.H., A. Abdusalam& E.S. Fahmy. Adomian decomposition method for nonlinear reaction diffusion system of Lotka-Volterra type. International Mathematical Forum. 2: 87-96 (2007)

Cherniha, R. &R.K. John. Non-linear reaction-diffusion systems with variable diffusivities: Lie symmetries, ansatz and exact solutions.Journal of Mathematical Analysis and Applications. 308: 11-35(2005)

Lotka, A.J.. Contribution to the theory of periodic reaction.Journalof Physical Chemistry. 14(3): 271-274, (1910)

Murray, J.D.. Mathematical Biology I. An introduction. Springer-Verlag Berlin Heidelberg, (2002)

Voltera, V. Variations and fluctuations of the number of the individuals in animal species living together.Animal Ecology(1926)

Wahab, H.A., M. Shakil, T. Khan, S. Bhatti&M. Naeem. A comparative study of a system of Lotka-Voltera type of PDEs through perturbation methods. Computational Ecology and Software. 3(4): 110-125, (2013)

Wahab, H.A., S. Bhatti& M. Naeem. A comparison of perturbation techniques for nonlinear problems.Journal of Prime Research in Mathematics, 10:59-79(2015)

Wahab, H.A., A. Jamal, S. Bhatti, M. Naeem, M. Shahzad& S. Hussain. Application of homotopy perturbation method to the navier-stokes equations in cylindrical coordinates.Computational Ecology and Software 5(2):139-151(2015)

Wahab,H.A., S. Hussain, S. Bhatti& M. Naeem. Mixed convection flow of powell-eyring fluid over a stretching cylinder with newtonian heating.Kuwait Journal of Science, (Accepted) (2015)


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