Recently, global and local relaxation Runge–Kutta methods have been developed for guaranteeing the conservation, dissipation, or other solution properties general convex functionals whose dynamics are crucial an ordinary differential equation solution. These novel time integration procedures application in a wide range of problems that require dynamics-consistent stable numerical methods. The s...

<p style='text-indent:20px;'>Classical symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation where all the terms in discrete Lagrangian are treated with same quadrature formula. We construct family of allowing use different formulas (primary and secondary) for Lagrangian. In particular, we study using Lobatto (with corresponding IIIA-B pair) as primary ...