Strong stability preserving high-order time discretization methods
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Strong stability preserving high-order time discretization methods

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Published by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor in Hampton, VA, Springfield, VA .
Written in English

Subjects:

  • Time dependence.,
  • Partial differential equations.,
  • TVD schemes.,
  • Discretization (Mathematics),
  • Numerical stability.,
  • Approximation.,
  • Runge-kutta method.

Book details:

Edition Notes

Other titlesStrong stability preserving high order time discretization methods.
StatementSigal Gottlief, Chi-Wang Shu, and Eitan Tadmor.
SeriesICASE report -- no. 2000-15., [NASA contractor report] -- NASA/CR-210093., NASA contractor report -- NASA CR-210093.
ContributionsShu, Chi-Wang., Tadmo, Eitan., Institute for Computer Applications in Science and Engineering.
The Physical Object
FormatMicroform
Pagination1 v.
ID Numbers
Open LibraryOL17717465M

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Previously termed TVD (total variation diminishing) time discretizations, these high-order time discretization methods preserve the strong stability properties of first-order Euler time stepping and have proved very useful, especially in solving hyperbolic partial differential : GottliebSigal, ShuChi-Wang, TadmorEitan. In this paper we review and further develop a class of strong stability-preserving (SSP) high-order time discretizations for semidiscrete method of lines approximations of partial differential equations. Previously termed TVD (total variation. We would like to show you a description here but the site won’t allow more. Strong Stability-Preserving High-Order Time Discretization Methods.

R.J. Spiteri, S.J. Ruuth, A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal. 40, – () . In this paper, we review and further develop a class of high-order strong-stability preserving (SSP) time discretization methods for the semi-discrete method-of-lines approximations of PDEs. This class of time discretization methods was first developed in [19] and [18] and was termed TVD (Total Variation Diminishing) time discretizations. To improve the accuracy of the scheme in time, we use the strong stability preserving (SSP), also referred to as total variation diminishing (TVD), high order Runge-Kutta time discretization. In the Lagrangian framework, it has the following form [6]. Strong stability preserving (SSP) high order time discretizations were developed to ensure nonlinear stability properties necessary in the numerical solution of hyperbolic partial differential equations with discontinuous solutions. SSP methods preserve the strong stability properties—in any norm, seminorm or convex functional—of the spatial discretization coupled with first order Euler.

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties-in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. The idea behind strong stability preserving methods is to begin with a method of lines semi-discretization that is strongly stable in a certain norm, semi-norm, or convex functional under forward Euler time stepping, when the timestep ∆ t is suitably restricted, and then try. A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods Article (PDF Available) in SIAM Journal on Numerical Analysis 40(2) February with Reads. elop a class of high order strong stabilit y preserving (SSP) time discretization metho ds for the semi-discrete metho d of lines appro ximations of PDEs. This class of time discretization metho ds w as rst dev elop ed in [19] and [18 ] and w as termed TVD (T otal V ariation Diminishing) time discretizations. It w as further dev elop ed in [6.