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

Felice Iavernaro, Francesca Mazzia
2021 Mathematics  
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
more » ... ms. 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.
doi:10.3390/math9101103 fatcat:7tndudhpurfixcjtu76i2p3jlu