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New Rosenbrock methods of order 3 for PDAEs of index 2. (English) Zbl 1162.65386
Summary: Motivated by solving the incompressible Navier-Stokes equations, the authors develop new Rosenbrock methods for index 2 partial differential-algebraic equations (PDAEs). Based on a well-known set of order conditions, solvers of order 3 with 4 internal stages are constructed. In particular, the methods allow the use of inexact Jacobians and approximations of \(\partial f/\partial t\). This leads to an important advantage in the robustness of the solvers with respect to the practical computation of these terms. At the end of the paper, five test problems of different severity and complexity are presented. They show the performance of the new methods in comparison with other Rosenbrock-solvers.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65R10 Numerical methods for integral transforms
65L80 Numerical methods for differential-algebraic equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65Y20 Complexity and performance of numerical algorithms
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