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

TL;DR

This paper introduces two new Rosenbrock-type numerical methods, Rodas6P and Tsit5DA, for solving index-1 differential algebraic equations, with improved accuracy and verified theoretical properties.

Contribution

The paper presents two novel Rosenbrock methods, including a sixth-order and a fifth-order method, enhancing the numerical solution of index-1 DAEs.

Findings

Rodas6P achieves sixth-order accuracy.

Tsit5DA provides a fifth-order solution with improved performance.

Theoretical properties are confirmed through tests and benchmarks.

Abstract

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.