A Symplectic Structure Preserved by the Trapezoidal Rule

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概要

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• The trapezoidal rule has often been referred to as being symmetric or time-reversible and is therefore good for Hamdtontan systems. However, it is well-known that the trapezoidal rule is not symplectic, but is related to the mid-point rule (which is symplectic) through a coordinate transformation. In this paper, we show that the trapezoidal rule preserves a symplectic structure different from the original one by O(h^2). The ideas in this paper also motivate us to apply Richardson's extrapolation to the trapezoidal rule. Numerical results show that the extrapolated trapezoidal rule preserves the Hamiltonian up to O(h^4).

• 社団法人日本物理学会の論文
• 2003-09-15

著者

• Wang Dao

  State Key Lab Of Scientific And Engineering Computing Institute Of Computational Mathematics And Sci

• TAM H.

  Department of Computer Science, Hong Kong Baptist University

• TAM H

  Department of Computer Science, Hong Kong Baptist University

• Tam H

  Department Of Computer Science Hong Kong Baptist University

関連論文

• A Symplectic Structure Preserved by the Trapezoidal Rule
• A Symplectic Structure Preserved by the Trapezoidal Rule

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