Geodesic
Solution of the tumor-immune system by differential transform method
Kassem, Mohamed Abd El Hady 1 ; Hemeda, A. A. 1 ; Abdeen, M. A. 1
1 Department of Mathematics, Faculty of Science, Tanta University, Egypt
Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 1, p. 9-21.

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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 Runge-Kutta second-third order method, in any interval we need.
DOI : 10.22436/jnsa.013.01.02
Classification : 37N30
Keywords: Kuznetsov and Taylor's model, differential transform method, Runge-Kutta fourth-fifth order method, Runge-Kutta second-third order method, tumor-immune system

Kassem, Mohamed Abd El Hady  1 ; Hemeda, A. A.  1 ; Abdeen, M. A.  1

1 Department of Mathematics, Faculty of Science, Tanta University, Egypt 
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Kassem, Mohamed Abd El Hady ; Hemeda, A. A. ; Abdeen, M. A. . Solution of the tumor-immune system by differential transform method. Journal of nonlinear sciences and its applications, Tome 13 (2020) no. 1, p. 9-21. doi : 10.22436/jnsa.013.01.02. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.013.01.02/

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