Gerd Steinebach | Searcharxiv

arXiv2026

Construction of DAE solver Rodas4PW and numerical test examples with Rosenbrock and W-methods in OrdinaryDiffEqRosenbrock.jl

This paper compares various Rosenbrock and Rosenbrock W-methods. To achieve this, some methods implemented in the Julia package OrdinaryDiffEqRosenbrock.jl are selected and benchmarked using test examples. The test examples include stiff ODE problems as well as differential-algebraic equations. In addition to the already known methods, the new W-method Rodas4PW is introduced and included in the tests.

math.NA↗

arXiv2025

Rodas6P and Tsit5DA - two new Rosenbrock-type methods for DAEs

Two new Rosenbrock methods for solving index-1 differential algebraic equations are presented. Rodas6P is a sixth-order method based on the same design principles as the Rodas3P, Rodas4P, and Rodas5P methods. Tsit5DA is based on an explicit solution approach for the differential equations and a linear-implicit approach for the algebraic equations. Such a fourth-order method has already been presented in Rentrop, Roche & Steinebach, 1989. Tsit5DA now provides a significantly improved fifth-order method which is based on the well known Tsit5 method. The theoretical properties of the new methods are verified by some order tests and benchmarks.

math.NA↗