Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
A note on splitting errors for advection-reaction equations
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
Global Error Estimates for Ordinary Differential Equations
ACM Transactions on Mathematical Software (TOMS)
A note on iterated splitting schemes
Journal of Computational and Applied Mathematics
Additive and iterative operator splitting methods and their numerical investigation
Computers & Mathematics with Applications
On the Richardson Extrapolation as Applied to the Sequential Splitting Method
Large-Scale Scientific Computing
Stability of the Richardson Extrapolation applied together with the θ-method
Journal of Computational and Applied Mathematics
Efficient implementation of stable Richardson Extrapolation algorithms
Computers & Mathematics with Applications
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During numerical time integration, the accuracy of the numerical solution obtained with a given step size often proves unsatisfactory. In this case one usually reduces the step size and repeats the computation, while the results obtained for the coarser grid are not used. However, we can also combine the two solutions and obtain a better result. This idea is based on the Richardson extrapolation, a general technique for increasing the order of an approximation method. This technique also allows us to estimate the absolute error of the underlying method. In this paper we apply Richardson extrapolation to the sequential splitting, and investigate the performance of the resulting scheme on several test examples.