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

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