Approximate analytical solutions for mathematical model of tumour invasion and metastasis using modified Adomian decomposition and homotopy perturbation methods. (English) Zbl 1406.35435

Mahiddin, Norhasimah; Ali, S. A. Hashim

J. Appl. Math. 2014, Article ID 654978, 13 p. (2014).

Summary: 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.

MSC:

35Q92	PDEs in connection with biology, chemistry and other natural sciences
92C50	Medical applications (general)
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
92C37	Cell biology