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 bound-ary 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.

A fourth order symplectic and conjugate-symplectic extension of the midpoint and trapezoidal methods

Iavernaro F.;Mazzia F.
2021-01-01

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 bound-ary 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/379853
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