2024-07-12 –, If (1.1)
Rosenbrock methods are known to be efficient within OrdinaryDiffEq.jl for stiff ODEs and DAEs in mass matrix form. This is especially true if the dimension of the problem is not too high or the evaluation of the Jacobian matrix of the right-hand side of the differential equation system is not too expensive.
There are implementations of many different Rosenbrock and Rosenbrock-W methods. In the talk we want to give an overview, present new methods and show some benchmarks and applications.
Currently, more than 30 Rosenbrock-type methods are implemented in the widely used Julia package OrdinaryDiffEq.jl. We discuss the differences and similarities of the various methods and explain why there is room for further improvements. In particular, this concerns the solution of time dependent algebraic equations and continuous output within the solution of DAE problems.
We present new methods Rodas23W and Rodas3P that are equipped with an error control of the interpolation. We compare this approach with alternative concepts such as residual control or modification of the stiffly accurate embedded method of Rodas5P, we perform some
benchmarks and present an application in the field of energy network simulation.
Gerd Steinebach is Professor of Mathematics at Bonn-Rhein-Sieg University of Applied Sciences. He teaches mathematical foundations, modelling and simulation in the Department of Engineering and Communication. His research interests lie in the field of numerical methods for differential equation systems and their applications. In particular, he focuses on mathematical modelling and simulation of water, gas and energy networks.