Abstract
In this paper we will introduce the concept of adjoint methods and some properties of them. We will show that there is a self-adjoint scheme of even order corresponding to every method. Using the self-adjoint schemes with lower order, we can construct higher order schemes by “composing” a method, and this constructing process can be continued to get arbitrary even order schemes. The “composing” method presented here can be used to non-symplectic schemes as well as symplectic ones.
Zusammenfassung
In dieser Arbeit führen wir den Begriff des adjungierten Verfahrens und einige seiner Eigenschaften ein. Zu jedem Verfahren gibt es ein selbst-adjungiertes Verfahren gerader Ordnung. Aus selbst-adjungierten Verfahren niedriger Ordnung können wir solche höherer Ordnung zusammensetzen, und dieser Konstruktionsprozeß kann bis zu beliebigen geraden Ordnungen fortgesetzt werden. Dieser Konstruktionsprozeß kann auch auf nicht-symplektische Verfahren angewandt werden.
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Meng-Zhao, Q., Wen-Jie, Z. Construction of higher order symplectic schemes by composition. Computing 47, 309–321 (1992). https://doi.org/10.1007/BF02320199
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DOI: https://doi.org/10.1007/BF02320199