COMMAX 2020 UiTM Kampus Kuala Terengganu

Ordinary differential equation (ODE) have very important applications and is a powerful tool in the study of many problems in the natural sciences and in technology. The reason for this is the fact that the objective laws governing certain phenomena (process) can be written as ODE. Thus, the ODEs are a quantitative expression of these processes. Many problems in real life such as chemistry, physics, ecology, economics, and biology can be modelled by systems of ODE. In solving the ODE, numerical methods are very important because most realistic systems of ODE cannot be solved analytically (Bildik, Necdet, & Deniz, 2015).

Therefore, in this project, four numerical methods which are Euler method, Improved Euler method, fourth order Runge-Kutta (RK4) method, and Runge-Kutta Fehlberg (RKF45) method were compared to solve first order ODE with initial value problems (IVP) numerically. Four type of first order ODE will have a test function with IVP. Those ODE are separable ODE, linear ODE, Bernoulli ODE, and a system of ODE. The exact solution for each test functions will be solved analytically.

All four numerical methods mentioned above will solve for the approximate solutions for each test functions. Three different step size will be used for each numerical method in order to observe the effects of step size to the accuracy of approximate solution and CPU time. The approximate solution will be compared to the exact solution and the relative error will be recorded. The best numerical method to approximate the solution for first order ODE with IVP can be determined from this project.