An improved Talbot method for numerical Laplace transform inversion
The classical Talbot method for the computation of the inverse Laplace transform is improved for the case where the transform is analytic in the complex plane except for the negative real axis. First, by using a truncated Talbot contour rather than the classical contour that goes to infinity in the...
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| creator | Dingfelder, Benedict Weideman, J. A. C |
| description | The classical Talbot method for the computation of the inverse Laplace
transform is improved for the case where the transform is analytic in the
complex plane except for the negative real axis. First, by using a truncated
Talbot contour rather than the classical contour that goes to infinity in the
left half-plane, faster convergence is achieved. Second, a control mechanism
for improving numerical stability is introduced. These two features are
incorporated into a software code, whose performance is assessed on transforms
from tables as well as from actual applications. It is shown that even when the
transform has singularities off the negative real axis, rapid convergence can
still be achieved in many cases. |
| doi_str_mv | 10.48550/arxiv.1304.2505 |
| format | Article |
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transform is improved for the case where the transform is analytic in the
complex plane except for the negative real axis. First, by using a truncated
Talbot contour rather than the classical contour that goes to infinity in the
left half-plane, faster convergence is achieved. Second, a control mechanism
for improving numerical stability is introduced. These two features are
incorporated into a software code, whose performance is assessed on transforms
from tables as well as from actual applications. It is shown that even when the
transform has singularities off the negative real axis, rapid convergence can
still be achieved in many cases.</description><identifier>DOI: 10.48550/arxiv.1304.2505</identifier><language>eng</language><subject>Mathematics - Numerical Analysis</subject><creationdate>2013-04</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1304.2505$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1304.2505$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Dingfelder, Benedict</creatorcontrib><creatorcontrib>Weideman, J. A. C</creatorcontrib><title>An improved Talbot method for numerical Laplace transform inversion</title><description>The classical Talbot method for the computation of the inverse Laplace
transform is improved for the case where the transform is analytic in the
complex plane except for the negative real axis. First, by using a truncated
Talbot contour rather than the classical contour that goes to infinity in the
left half-plane, faster convergence is achieved. Second, a control mechanism
for improving numerical stability is introduced. These two features are
incorporated into a software code, whose performance is assessed on transforms
from tables as well as from actual applications. It is shown that even when the
transform has singularities off the negative real axis, rapid convergence can
still be achieved in many cases.</description><subject>Mathematics - Numerical Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz7tqxDAUBFA1KcImfapFP2BHtnTlVbmYvMCQxr25ehGBJRnZMcnfZzdJNcUMA4eQh4bV4gTAHrF8hb1uOBN1CwxuSX9ONMSl5N1ZOuKs80aj2z6ypT4Xmj6jK8HgTAdcZjSObgXTeqkiDWl3ZQ053ZEbj_Pq7v_zQMbnp7F_rYb3l7f-PFQoASrleWelQsZZw7XwnVVGS_BKWTxB17Zdoy3vmAdsnWDCC6GZAjRGXvaS8wM5_t3-IqalhIjle7pipiuG_wCjykRh</recordid><startdate>20130409</startdate><enddate>20130409</enddate><creator>Dingfelder, Benedict</creator><creator>Weideman, J. A. C</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20130409</creationdate><title>An improved Talbot method for numerical Laplace transform inversion</title><author>Dingfelder, Benedict ; Weideman, J. A. C</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a655-9f37d69a03013b4f7d9cb65f99da8572271bd370f5a2e404f44b095acc613b633</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Mathematics - Numerical Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Dingfelder, Benedict</creatorcontrib><creatorcontrib>Weideman, J. A. C</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Dingfelder, Benedict</au><au>Weideman, J. A. C</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An improved Talbot method for numerical Laplace transform inversion</atitle><date>2013-04-09</date><risdate>2013</risdate><abstract>The classical Talbot method for the computation of the inverse Laplace
transform is improved for the case where the transform is analytic in the
complex plane except for the negative real axis. First, by using a truncated
Talbot contour rather than the classical contour that goes to infinity in the
left half-plane, faster convergence is achieved. Second, a control mechanism
for improving numerical stability is introduced. These two features are
incorporated into a software code, whose performance is assessed on transforms
from tables as well as from actual applications. It is shown that even when the
transform has singularities off the negative real axis, rapid convergence can
still be achieved in many cases.</abstract><doi>10.48550/arxiv.1304.2505</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Numerical Analysis |
| title | An improved Talbot method for numerical Laplace transform inversion |
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