%0 Journal Article %1 sportisse2000analysis %A Sportisse, Bruno %D 2000 %J Journal of Computational Physics %K 34a30-linear-odes-and-systems-general 34e15-odes-singular-perturbations 35k15-ivps-second-order-parabolic-problems 65l05-odes-ivps 65m20-pdes-ivps-method-of-lines 80a25-combustion 80m20-heat-transfer-finite-difference-methods 92d40-ecology 92e20-chemistry-classical-flows-reactions %N 1 %P 140-168 %R 10.1006/jcph.2000.6495 %T An Analysis of Operator Splitting Techniques in the Stiff Case %U https://www.sciencedirect.com/science/article/pii/S0021999100964957 %V 161 %X Operator splitting methods are commonly used in many applications. We focus here on the case where the evolution equations to be simulated are stiff. We will more particularly consider the case of two operators: a stiff one and a nonstiff one. This occurs in numerous application fields (e.g., combustion, air pollution, and reactive flows). The classical analysis of the splitting error may then fail, since the chosen splitting timestep Δt is in practice much larger than the fastest time scales: the asymptotic expansion Δt→0 is therefore no longer valid. We show here that singular perturbation theory provides an interesting framework for the study of splitting error. Some new results concerning the order of local errors are derived. The main result deals with the choice of the sequential order for the operators: the stiff operator must always be last in the splitting scheme.

@article{sportisse2000analysis, abstract = {Operator splitting methods are commonly used in many applications. We focus here on the case where the evolution equations to be simulated are stiff. We will more particularly consider the case of two operators: a stiff one and a nonstiff one. This occurs in numerous application fields (e.g., combustion, air pollution, and reactive flows). The classical analysis of the splitting error may then fail, since the chosen splitting timestep Δt is in practice much larger than the fastest time scales: the asymptotic expansion Δt→0 is therefore no longer valid. We show here that singular perturbation theory provides an interesting framework for the study of splitting error. Some new results concerning the order of local errors are derived. The main result deals with the choice of the sequential order for the operators: the stiff operator must always be last in the splitting scheme.}, added-at = {2021-02-11T23:58:19.000+0100}, author = {Sportisse, Bruno}, biburl = {https://www.bibsonomy.org/bibtex/23123e81b65c15fd1aa8c8bdc0e4aa4b0/gdmcbain}, doi = {10.1006/jcph.2000.6495}, interhash = {66ab849d6d018399f956986b113a793f}, intrahash = {3123e81b65c15fd1aa8c8bdc0e4aa4b0}, issn = {0021-9991}, journal = {Journal of Computational Physics}, keywords = {34a30-linear-odes-and-systems-general 34e15-odes-singular-perturbations 35k15-ivps-second-order-parabolic-problems 65l05-odes-ivps 65m20-pdes-ivps-method-of-lines 80a25-combustion 80m20-heat-transfer-finite-difference-methods 92d40-ecology 92e20-chemistry-classical-flows-reactions}, number = 1, pages = {140-168}, timestamp = {2021-02-11T23:58:19.000+0100}, title = {An Analysis of Operator Splitting Techniques in the Stiff Case}, url = {https://www.sciencedirect.com/science/article/pii/S0021999100964957}, volume = 161, year = 2000 }