Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Time integration of the shallow water equations in spherical geometry
Journal of Computational Physics
Parallel 'Peer' two-step W-methods and their application to MOL-systems
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
An anelastic allspeed projection method for gravitationally stratified flows
Journal of Computational Physics
Explicit two-step peer methods
Computers & Mathematics with Applications
Superconvergent explicit two-step peer methods
Journal of Computational and Applied Mathematics
High-order linearly implicit two-step peer -- finite element methods for time-dependent PDEs
Applied Numerical Mathematics
Parameter optimization for explicit parallel peer two-step methods
Applied Numerical Mathematics
Rosenbrock-type 'Peer' two-step methods
Applied Numerical Mathematics
Partially implicit peer methods for the compressible Euler equations
Journal of Computational Physics
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When cut cells are used for the representation of orography this leads to very small cells. For explicit methods this results in very harsh time step restrictions due to the CFL criterion. Therefore we consider linearly implicit peer methods for the integration of the compressible Euler equations. To be more efficient we use a simplified Jacobian. We present a linear stability theory which takes the effects of this simplified Jacobian in account. The developed second-order two-stage peer method is A-stable not only in the common sense but also when using the simplified Jacobian and retains the order independently of the Jacobian. In numerical tests the presented method produces good results even with time steps 100 times larger than explicit schemes could stably use.