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.
KeywordsCollocation Method Euler Method Adjoint Method Kepler Problem Composition Method
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- 1.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.Google Scholar