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Strong stability preserving methods

Strong Stability Preserving Methods. For nonlinear nonautonomous systems:. For linear, autonomous systems:. This website was developed by David Ketcheson, Daniel Higgs, and Sigal Gottlieb and is currently maintained by Daniel Higgs. The development of the methods in this web site and the numerical test suite. Were partially supported by funding from AFOSR grant numbers. And by KAUST grant number FIC/2010/05. Thursday, 13-Aug-2015 22:15:08 MDT.

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Strong stability preserving methods | sspmethods.org Reviews

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Strong Stability Preserving Methods. For nonlinear nonautonomous systems:. For linear, autonomous systems:. This website was developed by David Ketcheson, Daniel Higgs, and Sigal Gottlieb and is currently maintained by Daniel Higgs. The development of the methods in this web site and the numerical test suite. Were partially supported by funding from AFOSR grant numbers. And by KAUST grant number FIC/2010/05. Thursday, 13-Aug-2015 22:15:08 MDT.

<META> KEYWORDS

1 optimized methods

2 explicit methods

3 runge kutta

4 multistep

5 multistep multistage msrk

6 implicit methods

7 matlab scripts

8 paper scripts

9 test suite

10 bibliography

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Strong stability preserving methods | sspmethods.org Reviews

https://sspmethods.org

Strong Stability Preserving Methods. For nonlinear nonautonomous systems:. For linear, autonomous systems:. This website was developed by David Ketcheson, Daniel Higgs, and Sigal Gottlieb and is currently maintained by Daniel Higgs. The development of the methods in this web site and the numerical test suite. Were partially supported by funding from AFOSR grant numbers. And by KAUST grant number FIC/2010/05. Thursday, 13-Aug-2015 22:15:08 MDT.

INTERNAL PAGES

sspmethods.org

1

Implicit Runge-Kutta methods

http://www.sspmethods.org/irk_nl.html

Implicit SSP Runge-Kutta Methods for Nonlinear Systems. For linear, autonomous systems:. The backward Euler method is unconditionally SSP. Within the class of general linear methods, only first order methods can be unconditionally SSP.

2

Implicit Linear Multistep methods

http://www.sspmethods.org/ilmm_nl.html

Implicit SSP Linear Multistep Methods for Nonlinear Systems. For linear, autonomous systems:. SSP Coefficients of optimal methods. The backward Euler method is unconditionally SSP. Within the class of general linear methods, only first order methods can be unconditionally SSP. The implicit trapezoidal rule is optimal with coefficient c=2.

3

Multistep Multistage (MSRK) Methods

http://www.sspmethods.org/msrk.html

Multistep Multistage (MSRK) Methods. This page contains information about MSRK methods. Optimal methods were found. S = number of stages. K = number of steps. Each of these coefficient files contains the following variables:. Matrix containing the values of $a {ij}$. Matrix containing the values of $ hat{a} {ij}$. In addition, these files retain information from the numerical optimization procedure that determined the above values. Begin{align*} b T e = 1 theta T l. end{align*}$. Begin{array}{ l l l l l ...

4

Explicit Runge-Kutta methods

http://www.sspmethods.org/erk_lin.html

Explicit SSP Runge-Kutta Methods for Nonlinear Systems. For linear, autonomous systems:. Optimal first order explicit SSP Runge-Kutta methods consist simply of repeated forward Euler steps. These methods all have effective SSP coefficient equal to unity and are equivalent to simply using the forward Euler method. M$-Stage, Order $m$. M$-Stage, Order $m-1$.

5

ssp

http://www.sspmethods.org/sspbib.html

A Bellen, Z. Jackiewicz, and M. Zennaro. Contractivity of waveform relaxation Runge-Kutta iterations and related limit methods for dissipative systems in the maximum norm. SIAM Journal of Numerical Analysis. 31:499-523, 1994. [ bib. A Bellen and L. Torelli. Unconditional contractivity in the maximum norm of diagonally split Runge-Kutta methods. SIAM Journal of Numerical Analysis. 34:528-543, 1997. [ bib. 53:265-279, 2005. [ bib. 249:201-219, 2005. [ bib. SIAM Journal of Numerical Analysis. Sigal Gottlieb...

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Strong stability preserving methods

Strong Stability Preserving Methods. For nonlinear nonautonomous systems:. For linear, autonomous systems:. This website was developed by David Ketcheson, Daniel Higgs, and Sigal Gottlieb and is currently maintained by Daniel Higgs. The development of the methods in this web site and the numerical test suite. Were partially supported by funding from AFOSR grant numbers. And by KAUST grant number FIC/2010/05. Thursday, 13-Aug-2015 22:15:08 MDT.

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