Abstract
After having seen in Chap. I some simple numerical methods and a variety of numerical phenomena that they exhibited, we now present more elaborate classes of numerical methods. We start with Runge-Kutta and collocation methods, and we introduce discontinuous collocation methods, which cover essentially all high-order implicit Runge-Kutta methods of interest. We then treat partitioned Runge-Kutta methods and Nyström methods, which can be applied to partitioned problems such as Hamiltonian systems. Finally we present composition and splitting methods.
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References
The article Strang (1968) deals with spatial discretizations of partial differential equations such as ut = Aux + Buy. There, the functions f[i] typically contain differences in only one spatial direction.
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© 2002 Springer-Verlag Berlin Heidelberg
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Hairer, E., Wanner, G., Lubich, C. (2002). Numerical Integrators. In: Geometric Numerical Integration. Springer Series in Computational Mathematics, vol 31. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05018-7_2
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DOI: https://doi.org/10.1007/978-3-662-05018-7_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-05020-0
Online ISBN: 978-3-662-05018-7
eBook Packages: Springer Book Archive