December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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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 weighted ...
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