<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:11.0pt;
font-family:"Calibri",sans-serif;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
span.EmailStyle18
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="EN-US" link="blue" vlink="purple" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal">Matt, they seem to be provided in Butcher tableau form in the paper. One can register an RK method and use it.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">An example (for ARKIMEX) is here: https://petsc.org/release/src/ts/tutorials/ex19.c.html<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Emil<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">petsc-dev <petsc-dev-bounces@mcs.anl.gov> on behalf of Matthew Knepley <knepley@gmail.com><br>
<b>Date: </b>Wednesday, May 11, 2022 at 6:01 AM<br>
<b>To: </b>PETSc <petsc-dev@mcs.anl.gov><br>
<b>Subject: </b>[petsc-dev] Another SSP method<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal">Someone from my class requested<o:p></o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"> R. J. Spiteri, S. J. Ruuth, A new class of optimal high-order strong-stability-<br>
preserving time discretization methods, SIAM J. Numer. Anal. 40 (2002) 469-491.<br clear="all">
<o:p></o:p></p>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal">which is a fourth order, five stage method that we do not appear to have. How hard is this to add?<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"> Thanks,<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"> Matt<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<p class="MsoNormal">-- <o:p></o:p></p>
<div>
<div>
<div>
<div>
<div>
<div>
<div>
<p class="MsoNormal">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<o:p></o:p></p>
</div>
<div>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
<div>
<p class="MsoNormal"><a href="http://www.cse.buffalo.edu/~knepley/" target="_blank">https://www.cse.buffalo.edu/~knepley/</a><o:p></o:p></p>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</body>
</html>