Advertisement
Published in:
2021 | OriginalPaper | Chapter
19. Higher Order Methods
Author : Tobias Weinzierl
Published in: Principles of Parallel Scientific Computing
Publisher: Springer International Publishing
Abstract
To construct higher-order time stepping methods, we discuss two paradigms: On the one hand, we can write down an integral equation for the time stepping and construct more accurate integrators for the right-hand side. On the other hand, we can shoot multiple times into the future to obtain a guess for the additional terms from the Taylor expansion. The first approach leads to multistep methods, the second approach introduces the principles behind Runge-Kutta methods. After a brief discussion how to program arbitrary order Runge-Kutta once the Butcher tableau is known, we briefly sketch leapfrog-type methods which yield particularly elegant, second order methods for our N-body problem.
