Computational Methods for Physicists by Simon Sirca & Martin Horvat

Author:Simon Sirca & Martin Horvat
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

7.3 Explicit Methods of the Runge–Kutta Type

Methods of the Runge–Kutta (RK) type are the best known representatives of single-step methods. The solution is advanced in a sequence of short steps h like in the Euler methods, but the right-hand side of the differential equation (7.1) is evaluated at particular intermediate points within each time step; by a suitable combination of these auxiliary quantities we wish the method to attain higher precision. The solution value at the next point of a step is computed as

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