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Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems

In: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

Author

Listed:
  • Xinyuan Wu

    (Nanjing University, Department of Mathematics
    Qufu Normal University, School of Mathematical Sciences)

  • Bin Wang

    (Qufu Normal University, School of Mathematical Sciences)

Abstract

In recent decades, the numerical simulation for nonlinear oscillators has received much attention and a large number of integrators for oscillatory problems have been developed. In this chapter, based on the continuous finite element approach, we propose and analyse new energy-preserving functionally-fitted, in particular, trigonometrically-fitted methods of an arbitrarily high order for solving oscillatory nonlinear Hamiltonian systems with a fixed frequency. In order to implement these new methods in an accessable and efficient style, they are formulated as a class of continuous-stage Runge–Kutta methods. The numerical results demonstrate the remarkable accuracy and efficiency of the new methods compared with the existing high-order energy-preserving methods in the literature.

Suggested Citation

  • Xinyuan Wu & Bin Wang, 2018. "Functionally Fitted Continuous Finite Element Methods for Oscillatory Hamiltonian Systems," Springer Books, in: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, chapter 0, pages 1-28, Springer.
    • Handle: RePEc:spr:sprchp:978-981-10-9004-2_1
    DOI: 10.1007/978-981-10-9004-2_1
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