Many complex nonlinear problems in science, economics, and engineering
require computers to solve and simulate mathematical models describing them. Hence, it
becomes extremely necessary to apply numerical methods to solve such problems. In
this chapter, numerical methods for solving initial value problems are considered. Taylor
series, Euler, Modified Euler’s, Runge-Kutta, Adams-Bash forth-Moulton and Milne
numerical methods are considered together with some Maple examples given. Numerical
simulations are designed and implemented using Maple software for HIV/AIDS,
Fitzhugh, and Fitzhugh-Nagumo, sickle cell anemia, zooplankton-fish, Gompertz tumor
and neural firing models. The Explore facility in Maple 2022 is utilized to design sliders
for investigating the behaviors of solutions of some ordinary differential equations
subject to parameter change.
Keywords: Codes, Convergence, Fitzhugh, Fish models, Fitzhugh-Nagumo, Maple solution, Numerical, HIV/AIDS, Solutions, Stability, Sickle cell anemia, Tumor, Zooplankton.
