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Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

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  • Norhasimah Mahiddin
  • S. A. Hashim Ali

Abstract

The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.

Suggested Citation

  • Norhasimah Mahiddin & S. A. Hashim Ali, 2014. "Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:654978
    DOI: 10.1155/2014/654978
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    1. Hashim, I. & Noorani, M.S.M. & Ahmad, R. & Bakar, S.A. & Ismail, E.S. & Zakaria, A.M., 2006. "Accuracy of the Adomian decomposition method applied to the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1149-1158.
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