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Composition Scheme

In: Symplectic Geometric Algorithms for Hamiltonian Systems

Author

Listed:
  • Kang Feng

    (Institute of Computational Mathematics and Scientific/Engineering Computing)

  • Mengzhao Qin

    (Institute of Computational Mathematics and Scientific/Engineering Computing)

Abstract

In this chapter, we consider a class of reversible schemes also called symmetrical schemes. In algebraic language, it is not other, just like self-adjoint schemes. Here, we only deal with one-step reversible schemes. We will introduce the concept of adjoint methods and some of their properties. We will show that there is a self-adjoint scheme of even order in 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 obtain arbitrary even order schemes. The composing method presented here can be used to in both non-symplectic and symplectic schemes.

Suggested Citation

  • Kang Feng & Mengzhao Qin, 2010. "Composition Scheme," Springer Books, in: Symplectic Geometric Algorithms for Hamiltonian Systems, chapter 0, pages 365-406, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-01777-3_9
    DOI: 10.1007/978-3-642-01777-3_9
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