Application of collocation method for solving a parabolic‐hyperbolic free boundary problem which models the growth of tumor with drug application |
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Authors: | Sakine Esmaili M. R. Eslahchi |
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Affiliation: | Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran |
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Abstract: | In this article, we want to solve a free boundary problem which models tumor growth with drug application. This problem includes five time dependent partial differential equations. The tumor considered in this model consists of three kinds of cells, proliferative cells, quiescent cells, and dead cells. Three different first‐order hyperbolic equations are given that describe the evolution of cells and other two second‐order parabolic equations describe the diffusion of nutrient and drug concentration. We solve the problem using the collocation method. Then, we prove stability and convergence of method. Also, some examples are considered to show the efficiency of method. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | collocation method parabolic‐hyperbolic equation free boundary problem tumor growth fixed point theory stability and convergence |
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