Solution of the tumor-immune system by differential transform method
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Authors
Mohamed Abd El Hady Kassem
- Department of Mathematics, Faculty of Science, Tanta University, Egypt.
A. A. Hemeda
- Department of Mathematics, Faculty of Science, Tanta University, Egypt.
M. A. Abdeen
- Department of Mathematics, Faculty of Science, Tanta University, Egypt.
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 Runge-Kutta
second-third order method, in any interval we need.
Share and Cite
ISRP Style
Mohamed Abd El Hady Kassem, A. A. Hemeda, M. A. Abdeen, Solution of the tumor-immune system by differential transform method, Journal of Nonlinear Sciences and Applications, 13 (2020), no. 1, 9--21
AMA Style
Kassem Mohamed Abd El Hady, Hemeda A. A., Abdeen M. A., Solution of the tumor-immune system by differential transform method. J. Nonlinear Sci. Appl. (2020); 13(1):9--21
Chicago/Turabian Style
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 Applications, 13, no. 1 (2020): 9--21
Keywords
- Kuznetsov and Taylor's model
- differential transform method
- Runge-Kutta fourth-fifth order method
- Runge-Kutta second-third order method
- tumor-immune system
MSC
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