Accuracy and stability of splitting with stabilizing corrections

Authors:
Willem Hundsdorfer
Affiliations:
CWI, Kruislaan 413, P.O.Box 94079, 1090 GB Amsterdam, The Netherlands
Venue:
Applied Numerical Mathematics
Year:
2002

Citing 9
Cited 7

Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations

Numerische Mathematik
Implicit-explicit methods for time-dependent partial differential equations

SIAM Journal on Numerical Analysis
An implicit-explicit approach for atmospheric transport-chemistry problems

Applied Numerical Mathematics
Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations

Applied Numerical Mathematics - Special issue on time integration
On the stability of implicit-explicit linear multistep methods

Applied Numerical Mathematics - Special issue on time integration
A note on stability of the Douglas splitting method

Mathematics of Computation
Trapezoidal and midpoint splittings for initial-boundary value problems

Mathematics of Computation
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems

SIAM Journal on Scientific Computing
Fundamentals of Numerical Reservoir Simulation

Fundamentals of Numerical Reservoir Simulation

Operator splitting and approximate factorization for taxis-diffusion-reaction models

Applied Numerical Mathematics
Stability of ADI schemes applied to convection-diffusion equations with mixed derivative terms

Applied Numerical Mathematics
The LEM exponential integrator for advection-diffusion-reaction equations

Journal of Computational and Applied Mathematics
Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms

Applied Numerical Mathematics
Long time stability of four methods for splitting the evolutionary Stokes-Darcy problem into Stokes and Darcy subproblems

Journal of Computational and Applied Mathematics
Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms

Applied Numerical Mathematics
Rosenbrock-type methods with Inexact AMF for the time integration of advection-diffusion-reaction PDEs

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper contains a convergence analysis for the method of Stabilizing Corrections, which is an internally consistent splitting scheme for initial-boundary value problems. To obtain more accuracy and a better treatment of explicit terms several extensions are regarded and analyzed. The relevance of the theoretical results is tested for convection-diffusion-reaction equations.