Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
SIAM Journal on Scientific Computing
Fourth Order Chebyshev Methods with Recurrence Relation
SIAM Journal on Scientific Computing
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Parallel Two-Step W-Methods with Peer Variables
SIAM Journal on Numerical Analysis
Parallel 'Peer' two-step W-methods and their application to MOL-systems
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Mechanisms of coupling in river flow simulation systems
Journal of Computational and Applied Mathematics - Special issue: Selected papers from the 2nd international conference on advanced computational methods in engineering (ACOMEN2002) Liege University, Belgium, 27-31 May 2002
High-order linearly implicit two-step peer -- finite element methods for time-dependent PDEs
Applied Numerical Mathematics
High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Rosenbrock-type 'Peer' two-step methods
Applied Numerical Mathematics
Implicit parallel peer methods for stiff initial value problems
Applied Numerical Mathematics
Linearly-implicit two-step methods and their implementation in Nordsieck form
Applied Numerical Mathematics
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For many practical problems an efficient solution of the one-dimensional shallow-water equations (Saint-Venant equations) is important, especially when large networks of rivers, channels or pipes are considered. In order to test and develop numerical methods four test problems are formulated. These tests include the well-known dam break and hydraulic jump problems and two steady state problems with varying channel bottom, channel width and friction. The space discretization of the partial differential equations is based on a finite volume approach with central WENO interpolation and local Lax-Friedrich fluxes (Kurganov and Levy, 2000) [7]. For time-integration new linearly-implicit two-step peer methods of orders three and four are developed. These methods are especially adapted to the usage within the method of lines framework. They show a good performance compared to the well-established methods like ode15s, radau5 or rodasp.