New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index (Q2490364)

New Rosenbrock methods for ordinary differential equations, differential-algebraic equations; partial differential equations (PDEs) and partial differential-algebraic equations (PDAEs) of index 1 are presented. These solvers are of order 3, have 3 or 4 internal stages, and fulfil certain order conditions to obtain a better convergence if inexact Jacobians and approximations of \(\frac{\partial f}{\partial t}\) are used. A comparison of the five new methods with five other Rosenbrock solvers shows the advantages of the new methods. They are applied to several differential equations such as a PDE, an index-1 PDAE and the Navier-Stokes equations with different right-hand sides. The results are presented in pleasant figures. The numerically observed temporal order of convergence are also given for the different examples.