Solution of the tumor-immune system by differential transform method

Volume 13, Issue 1, pp 9--21 http://dx.doi.org/10.22436/jnsa.013.01.02
Publication Date: August 27, 2019 Submission Date: May 29, 2019 Revision Date: July 01, 2019 Accteptance Date: July 23, 2019

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.


Keywords


MSC


References