Advances in Differential Equations and Control Processes
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Abstract: Motivated by solving
the incompressible Navier-Stokes equations, the authors develop new Rosenbrock
methods for index 2 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 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.
Keywords and phrases: nonlinear parabolic equations, Rosenbrock methods, order reduction.
