A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
Journal of Computational Physics
Optimally-stable second-order accurate difference schemes for non-linear conservation laws in 3D
Applied Numerical Mathematics
MUSTA Fluxes for systems of conservation laws
Journal of Computational Physics
Volterra Algorithm for Modelling Sea Surface Current Circulation from Satellite Altimetry Data
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
On numerical realizability of thermal convection
Journal of Computational Physics
Optimally-stable second-order accurate difference schemes for non-linear conservation laws in 3D
Applied Numerical Mathematics
Multidimensional first and second order symmetric Strang splitting for hyperbolic systems
Applied Numerical Mathematics
A new TVD flux-limiter method for solving nonlinear hyperbolic equations
Journal of Computational and Applied Mathematics
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
International Journal of Innovative Computing and Applications
Transactions on Computational Science VI
International Journal of Computer Applications in Technology
Extrapolation-based implicit-explicit general linear methods
Numerical Algorithms
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Global composition of several time steps of the two-step Lax--Wendroff scheme followed by a Lax--Friedrichs step seems to enhance the best features of both, although it is only first order accurate. We show this by means of some examples of one-dimensional shallow water flow over an obstacle. In two dimensions we present a new version of Lax--Friedrichs and an associated second order predictor-corrector method. Composition of these schemes is shown to be effective and efficient for some two-dimensional Riemann problems and for Noh's infinite strength cylindrical shock problem. We also show comparable results for composition of the predictor-corrector scheme with a modified second order accurate weighted essentially nonoscillatory (WENO) scheme. That composition is second order but is more efficient and has better symmetry properties than WENO alone. For scalar advection in two dimensions the optimal stability of the new predictor-corrector scheme is shown using computer algebra. We also show that the generalization of this scheme to three dimensions is unstable, but by using sampling we are able to show that the composites are suboptimally stable.