First-Order Ordinary Differential Equations

Abstract

When one solves differential equations numerically one faces the problem of finding those solutions with as great an accuracy as possible in terms of the mesh-size of the net on which the reduction of the differential equation to a difference equation is carried out. At present many methods exist for finding approximate solutions with a given degree of accuracy when the solution of the differential equation is smooth. The Runge-Kutta method is one of the most widely used since it allows one to create an algorithm for the solution of the problem in a simple and straightforward manner. The theoretical foundations for the construction of the algorithm are well understood as well, making this a most attractive method of numerical mathematics.