Continuous Explicit Runge-Kutta methods

Forward and adjoint sensitivity analysis with continuous explicit Runge - Kutta methods ⋆

We study the numerical solution of tangent linear, first, and second order adjoint models with high-order explicit, continuous Runge-Kutta methods. The approaches currently implemented in popular packages such as SUNDIALS or DASPKADJOINT are based on linear multistep methods. For adaptive time integration of nonlinear models, interpolation of the forward model solution is required during the ad...

2-stage explicit total variation diminishing preserving Runge-Kutta methods

In this paper, we investigate the total variation diminishing property for a class of 2-stage explicit Rung-Kutta methods of order two (RK2) when applied to the numerical solution of special nonlinear initial value problems (IVPs) for (ODEs). Schemes preserving the essential physical property of diminishing total variation are of great importance in practice. Such schemes are free of spurious o...

DENSERKS: A suite of Fortran sensitivity solvers using continuous, explicit Runge-Kutta schemes

Implicit-Explicit Runge-Kutta Schemes for Numerical Discretization of Optimal Control Problems

Implicit-explicit (IMEX) Runge-Kutta methods play a major rule in the numerical treatment of differential systems governed by stiff and non-stiff terms. This paper discusses order conditions and symplecticity properties of a class of IMEX Runge–Kutta methods in the context of optimal control problems. The analysis of the schemes is based on the continuous optimality system. Using suitable trans...

A Survey of the Explicit Runge-Kutta Method

Research in explicit Runge-Kutta methods is producing continual improvements to the original algorithms, and the aim of this survey is to relate the current state-of-the-art. In drawing attention to recent advances, we hope to provide useful information for those who apply numerical methods. We describe recent work in the derivation of Runge-Kutta coeecients: \classical" general-purpose formula...