A Fourth Order Symplectic and Conjugate-Symplectic Extension of the Midpoint and Trapezoidal Methods

Felice Iavernaro and Francesca Mazzia
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Felice Iavernaro: Dipartimento di Matematica, Università degli studi di Bari Aldo Moro, 70125 Bari, Italy
Francesca Mazzia: Dipartimento di Informatica, Università degli studi di Bari Aldo Moro, 70125 Bari, Italy

Mathematics, 2021, vol. 9, issue 10, 1-15

Abstract: The paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting from the multi-derivative extension of the midpoint method we have obtained a new symmetric implicit Runge–Kutta method of order four, for the numerical solution of first-order differential equations. The new method is symplectic and is suitable for the solution of both initial and boundary value Hamiltonian problems. Moreover, starting from the conjugate class of multi-derivative trapezoidal schemes, we have derived a new method that is conjugate to the new symplectic method.

Keywords: ordinary differential equations; Hamiltonian systems; multi-derivative methods; simplectic methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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