Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Automatic differentiation of explicit Runge-Kutta methods for optimal control
Computational Optimization and Applications
On the discrete adjoints of adaptive time stepping algorithms
Journal of Computational and Applied Mathematics
FATODE: a library for forward, adjoint and tangent linear integration of stiff systems
Proceedings of the 19th High Performance Computing Symposia
Stability and consistency of discrete adjoint implicit peer methods
Journal of Computational and Applied Mathematics
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In this paper we analyze the consistency and stability properties of Runge-Kutta discrete adjoints. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis uses the concept of elementary differentials and reveals that the discrete Runge-Kutta adjoint method has the same order of accuracy as the original, forward method. A singular perturbation analysis reveals that discrete adjoints of stiff Runge-Kutta methods are well suited for stiff problems.