Solution of the tumor-immune system by differential transform method

Journal of Nonlinear Sciences and Applications Pub Date : 2019-08-27 DOI:10.22436/jnsa.013.01.02

M. Kassem, A. A. Hemeda, M. Abdeen

引用次数: 2

Abstract

In this paper, differential transform method (DTM) is presented to solve Tumor-immune system at two initial conditions where two different cases of the interaction between tumor cells and effector cells. The system is presented to show the ability of the method for non-linear systems of differential equations. By using small iteration, the results of DTM are near the results of Runge-Kutta fourth-fifth order method (ode45 solver in MATLAB) and better than the results of Runge-Kutta second-third order method (ode23 solver in MATLAB). Also, the residual error of DTM’s solutions approach zero. Therefore, DTM’s solutions approximate exact solutions. Finally, we conclude formulae that we can find DTM’s solutions, better than the results of RungeKutta second-third order method, in any interval we need.

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用微分变换法求解肿瘤免疫系统

针对肿瘤细胞与效应细胞相互作用的两种不同初始条件下的肿瘤免疫系统问题，提出了微分变换方法。通过实例验证了该方法对非线性微分方程组的求解能力。通过小迭代，DTM的结果接近龙格-库塔四阶五阶法(MATLAB中的ode45求解器)的结果，优于龙格-库塔二阶三阶法(MATLAB中的ode23求解器)的结果。DTM解的残差接近于零。因此，DTM的解近似于精确解。最后，我们得出公式，我们可以找到DTM的解，比RungeKutta二三阶方法的结果更好，在我们需要的任何区间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Sciences and Applications MATHEMATICS, APPLIED-MATHEMATICS

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期刊介绍： The Journal of Nonlinear Science and Applications (JNSA) (print: ISSN 2008-1898 online: ISSN 2008-1901) is an international journal which provides very fast publication of original research papers in the fields of nonlinear analysis. Journal of Nonlinear Science and Applications is a journal that aims to unite and stimulate mathematical research community. It publishes original research papers and survey articles on all areas of nonlinear analysis and theoretical applied nonlinear analysis. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Manuscripts are invited from academicians, research students, and scientists for publication consideration. Papers are accepted for editorial consideration through online submission with the understanding that they have not been published, submitted or accepted for publication elsewhere.