Runge-Kutta Methods and Applications

Abstract

The Initial value problems, IVPs are very important in modeling some real life problems. There are many analytical methods designed to solve IVPs. In practice these methods do not cover all types of problems. Thus, numerical methods are used. In this study a detailed description, with implementation, is given for the class of numerical methods known as Runge-Kutta methods. Both explicit and implicit methods are discussed. Full derivations of the methods are made. Different orders are used. Practical implementation of the methods are made using Matlab computational environment. These methods are used to solve some practical problems in Civil, Chemistry, Computer Engineering and physics.