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New Rosenbrock W-methods of order 3 for partial differential algebraic equations of index. (English) Zbl 1093.65097
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.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65L80 Numerical methods for differential-algebraic equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
35K55 Nonlinear parabolic equations
35R10 Partial functional-differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65L20 Stability and convergence of numerical methods for ordinary differential equations
35Q30 Navier-Stokes equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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