COMMAX 2020 UiTM Kampus Kuala Terengganu

ABSTRACT

Many models from Engineering, biological and physical sciences are used ordinary differential equations in their application. Thus, the needs for study of ordinary differential equations (ODE) are essential in order to determine the solutions. In this research, first order differential equations problems have been chosen to be solved theoretically and numerically. The theoretical method is recognized to have difficulty in obtaining exact solutions for most ODE problems. Thus, numerical method are efficient way to obtain approximate solutions to such differential equations. Numerical methods used in this research to solve ODE problems are modification of Euler methods such as Modified Euler method (ME), Improved Modified Euler method (IME), Modified Improved Modified Euler method (MIME) and Modified Euler Based on Harmonic Polygon method (HP). The purpose of this research is to discover which modification of Euler method that is the best and efficient method in solving ODE problems in terms of relative error. Relative error is the difference of the analytic solution and approximate solution. Therefore, in order to validate the efficiency and accuracy, the numerical solution are compared with the analytic solutions. In this research also different step size are being used in each numerical method where various step sizes will give impact to the solution. I observed that when the step size becomes smaller, the accuracy of the solution become more correct. The smaller step size also result in bigger iterations and longer CPU time. Among these four modified Euler methods observed that MIME offers better approximation compares to other methods.