Numerical Comparison of Runge-Kutta (Rk5) and New Iterative Method (Nim) for Solving Metastatic Cancer Model

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 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.