Numerical Methods for Solving Systems of Ordinary Differential Equations

ABSTRACT: This thesis concantrates on numerical methods for solving ordinary differential equations. Firstly, we discuss the concept of convergence, local-truncation error, globaltruncation error, consistency, types of stability, zero-stability, and weak-stability. Afterwards, we inform some materials for Euler and Runge-Kutta method. The given ordinary differential equation is analyzed on Euler and Runge-Kutta method to find the approximated solution with the given initial conditions. Then, the stability of each method is examined briefly. We also focus on numerical methods for systems. Then, the reason of the stiff system is discussed. After investigating the numerical methods, we gave advantages and disadvantages of Euler method and Fourth Order Runge-Kutta method. Finally, numerical experiments is applied on Explicit Euler method and Explicit Fourth Order Runge-Kutta method. The approximated solutions with different step-size and analytical solutions of methods are computed in Matlab software. The computation of approximated solutions of methods are compared with analytical solutions. Then we discussed the accuracy of these methods when they are applied to the specified system in Chapter 7. Finally, we conclude that Explicit Fourth Order Runge-Kutta method is more accurate than the Explicit Euler method. Keywords: Ordinary Differential Equations, Numerical solutions, Euler’s method, Runge-Kutta method, Stiff System ……………………………………………………………………………………………………………………………………………………………………………………………………………………