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Application of collocation method for solving a parabolic‐hyperbolic free boundary problem which models the growth of tumor with drug application
Author(s) -
Esmaili Sakine,
Eslahchi M. R.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4092
Subject(s) - mathematics , orthogonal collocation , collocation (remote sensing) , partial differential equation , convergence (economics) , hyperbolic partial differential equation , collocation method , parabolic partial differential equation , ftcs scheme , boundary value problem , boundary (topology) , stability (learning theory) , mathematical analysis , ordinary differential equation , differential equation , differential algebraic equation , computer science , machine learning , economic growth , economics
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.