Received November 1, 1962. Revised April 22, 1963. * If the function f(y) satisfies a Lipschitz condition and h is sufficiently small, then the equations defining g(1>, g(2), • • • , gw have a unique… Expand

A comparison is made of two stability criteria. The first is a modification to nonautonomous problems of A-stability and the second is a similar modification of B-stability. It is shown that under… Expand

This third edition of Numerical Methods for Ordinary Differential Equations will serve as a key text for senior undergraduate and graduate courses in numerical analysis, and is an essential resource for research workers in applied mathematics, physics and engineering.Expand

We consider a set of η first order simultaneous differential equations in the dependent variables y1, y2, …, yn and the independent variable x ⋮ No loss of gernerality results from taking the… Expand

A class of integration methods which includes Runge-Kutta methods, as well as the Picard successive approximation method, is shown to be related to a certain group which can be represented as the… Expand

For a class of methods sufficiently general as to include linear multistep and Runge-Kutta methods as special cases, a concept known as algebraic stability is defined, based on a non-linear test problem, which enables estimates of error growth to be provided.Expand

Numerical methods for the solution of the initial value problem ill ordinary differential equations fall mainly into two categories: multi-step methods and RungeKutta methods. For these and for some… Expand