COMMAX 2020 UiTM Kampus Kuala Terengganu

Numerical computations historically play a critical role in natural sciences and engineering. These days however, it is not only traditional, whether do digital humanities or biotechnology, design novel materials or build artificial intelligence systems, virtually any quantitative work involves some amount of numerical computing. An equation that relates one or more functions and their derivatives is differential equation. the functions generally represent physical quantities, in applications, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. For solving initial value problems for ordinary differential equations, there are many types of practical numerical methods. This project mainly presents Euler Method, second order Runge Kutta Method (RK2), third order Runge Kutta Method (RK3), fourth order Runge Kutta Method (RK4) and fifth order Runge Kutta Method (RK5) for solving initial value problems (IVP) for ordinary differential equations (ODE). The proposed methods are precise efficient and practically well suited for solving these problems. In order to verify the accuracy, compared numerical solutions with the error analysis. The numerical solutions are in good condition with the exact solutions. Comparison between CPU time and step sizes has been presented. The step size need to be very small in order to achieve higher accuracy in the solution. From this comparison, the best that can identify is fifth order of Runge Kutta Method than other method. Finally, to investigate the best  numerical for solving ODE problem.