Explicit stabilized multirate method for stiff differential equations

Abdulle, Assyr and Grote, Marcus J. and Rosilho de Souza, Giacomo. (2022) Explicit stabilized multirate method for stiff differential equations. Mathematics of Computation, 91 (338). pp. 2681-2714.

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Official URL: https://edoc.unibas.ch/93332/

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Stabilized Runge–Kutta methods are especially efficient for the numerical solution of large systems of stiff nonlinear differential equations because they are fully explicit. For semi-discrete parabolic problems, for instance, stabilized Runge–Kutta methods overcome the stringent stability condition of standard methods without sacrificing explicitness. However, when stiffness is only induced by a few components, as in the presence of spatially local mesh refinement, their efficiency deteriorates. To remove the crippling effect of a few severely stiff components on the entire system of differential equations, we derive a modified equation, whose stiffness solely depends on the remaining mildly stiff components. By applying stabilized Runge–Kutta methods to this modified equation, we then devise an explicit multirate Runge–Kutta–Chebyshev (mRKC) method whose stability conditions are independent of a few severely stiff components. Stability of the mRKC method is proved for a model problem, whereas its efficiency and usefulness are demonstrated through a series of numerical experiments.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Numerik (Grote)
UniBasel Contributors:Grote, Marcus J.
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Mathematical Society
Note:Publication type according to Uni Basel Research Database: Journal article
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edoc DOI:
Last Modified:01 Feb 2023 16:42
Deposited On:01 Feb 2023 16:42

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