NUMERICAL COMPARISON OF RUNGE-KUTTA (RK5) AND NEW ITERATIVE METHOD (NIM) FOR SOLVING METASTATIC CANCER MODEL
Falade Kazeem Iyanda1*,Tiamiyu Abd`Gafar Tunde2 and Umar Isa3
1,3Department of Mathematics, Faculty of Computing and Mathematical Sciences Kano
University of Science and Technology Wudil, P.M.B 3244 Kano State Nigeria,
2Department of Mathematics, Federal University of Technology, Minna Niger State Nigeria
This paper attempts to present and employ Runge-Kutta Method of fifth-order (RK5) and New Iterative Method for the numerical solution of metastatic cancer model which occur in two compartments of cancer environment. These methods have been proved to be powerful mathematical tools for various phenomena in biomathematics and it is extremely effective for linear and non-linear systems of differential equations. Our numerical experiments illustrate the effect of parameters β_1,β_2 and β_3 on cancer models which are responsible for the spread or reduction of cancer cells through the boundary of an organ tissue. The results obtained are compared with analytical solutions and show that (RK5) and NIM are powerful numerical techniques to solve systems of differential equations. Finally, all computations and algorithms are implemented using MAPLE 18 software version.
Keywords: Analytical solutions, MAPLE 18 Mathematical software, Metastatic cancer model, New Iterative Method (NIM), Runge-Kutta method (RK5).
Published On: 08 March 2021