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    188宝金博页面版: The method of lines for the numerical solution of a mathematical model for capillary formation The role of endothelial cells in

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    内容提示： The method of lines for the numerical solutionof a mathematical model for capillaryformation: The role of endothelialcells in the capillarySerdal Pamuka, * , Arzu Erdem baDepartment of Mathematics, University of Kocaeli, Umuttepe Campus, 41800 Kocaeli, TurkeybApplied Mathematical Sciences Research Center, University of Kocaeli, Ataturk Bulvari, 41300 Kocaeli, TurkeyAbstractIn this paper we present the method of lines to obtain the numerical solution of a mathematical model for capillaryformation in tumor a...

    文档格式：PDF | 页数：5 | 浏览次数：13 | 上传日期：2020-06-19 18:21:02 | 文档星级：
    The method of lines for the numerical solutionof a mathematical model for capillaryformation: The role of endothelialcells in the capillarySerdal Pamuka, * , Arzu Erdem baDepartment of Mathematics, University of Kocaeli, Umuttepe Campus, 41800 Kocaeli, TurkeybApplied Mathematical Sciences Research Center, University of Kocaeli, Ataturk Bulvari, 41300 Kocaeli, TurkeyAbstractIn this paper we present the method of lines to obtain the numerical solution of a mathematical model for capillaryformation in tumor angiogenesis. This method is an approach to the numerical solution of partial dif f erential equationsthat involve a time variable t and space variables x,y,... As the number of lines is increased, the accuracy of the methodof lines representation of the original system increases. The method provides very accurate numerical solutions for linearand nonlinear problems in comparison with other existing methods. We also provide computer programs written in Mat-lab and f i gures that show the endothelial cell movement.? 2006 Elsevier Inc. All rights reserved.Keywords: Method of lines; Capillary formation; Tumor angiogenesis; Numerical solution1. IntroductionWe consider the following initial boundary-value problem originally presented in [6]:ouot¼ DooxuooxlnufðxÞ? ? ? ?; ðx;tÞ 2 X T :¼ f0 < x < 1;0 < t 6 Tg; ð1Þuðx;0Þ ¼ 1; x 2 ð0;1Þ; ð2ÞDuooxlnufðxÞ?? ?x¼0¼ 0; t 2 ½0;T?; ð3ÞDuooxlnufðxÞ?? ?x¼1¼ 0; t 2 ½0;T?; ð4Þ0096-3003/$ - see front matter ? 2006 Elsevier Inc. All rights reserved.doi:10.1016/j.amc.2006.08.024*Corresponding author.E-mail addresses: spamuk@kou.edu.tr (S. Pamuk), aerdem@kou.edu.tr (A. Erdem).Applied Mathematics and Computation 186 (2007) 831–835www.elsevier.com/locate/amc

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