Unconditional Stability for Multistep ImEx Schemes: Theory
Author(s)Seibold, Benjamin; Shirokoff, David; Zhou, Dong; Rosales, Rodolfo
MetadataShow full item record
This paper presents a new class of high order linear ImEx (implicit-explicit) multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such splittings can arise, for example, in variable coefficient problems, or the incompressible Navier-Stokes equations. To characterize the new ImEx schemes, an unconditional stability region is introduced, which plays a role analogous to that of the stability region in conventional multistep methods. Moreover, computable quantities (such as a numerical range) are provided that guarantee an unconditionally stable scheme for a proposed ImEx matrix splitting. The new approach is illustrated with several examples. Coefficients of the new schemes up to fifth order are provided.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
SIAM Journal on Numerical Analysis
Society for Industrial & Applied Mathematics (SIAM)
Rosales, Rodolfo R., Benjamin Seibold, David Shirokoff, and Dong Zhou. “Unconditional Stability for Multistep ImEx Schemes: Theory.” SIAM Journal on Numerical Analysis 55, no. 5 (January 2017): 2336–2360. © 2017 Society for Industrial and Applied Mathematics.
Final published version