Advanced Engineering Mathematics, 7th Edition

6.2 Runge–Kutta Methods

INTRODUCTION

Probably one of the more popular, as well as most accurate, numerical procedures used in obtaining approximate solutions to a first-order initial-value problem y′ = f(x, y), y(x₀) = y₀ is the fourth-order Runge–Kutta method devised by the German applied mathematicians Carl David Runge (1856–1927) and Martin Wilhelm Kutta (1867–1944) in the late 1890s. As the words fourth-order suggest, there are Runge–Kutta methods of different orders.

Runge–Kutta Methods

Fundamentally, all Runge–Kutta methods are generalizations of the basic Euler formula (1) of Section 6.1 in that the slope function f is replaced by a ...