The Condition of Explicitness and the Diagonal Implicitness for Composition of Runge-Kutta Method with its Adjoint One

Abstract

The paper addresses three topics: the adjoint Runge-Kutta methods, the composition of several Runge - Kutta methods and symplectic partitioned Runge-Kutta methods. A connection between the explicitness or diagonal implicitness for adjoint Runge-Kutta methods and conditions of a partitioned symplectic Runge-Kutta methods.