RBF‐ENO/WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations
In this research, a class of radial basis functions (RBFs) ENO/WENO schemes with a Lax–Wendroff time discretization procedure, named as RENO/RWENO‐LW, for solving Hamilton–Jacobi (H–J) equations is designed. Particularly the multi‐quadratic RBFs are used. These schemes enhance the local accuracy and...
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| Veröffentlicht in: | Numerical methods for partial differential equations 2021-01, Vol.37 (1), p.594-613 |
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| container_title | Numerical methods for partial differential equations |
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| creator | Abedian, Rooholah Dehghan, Mehdi |
| description | In this research, a class of radial basis functions (RBFs) ENO/WENO schemes with a Lax–Wendroff time discretization procedure, named as RENO/RWENO‐LW, for solving Hamilton–Jacobi (H–J) equations is designed. Particularly the multi‐quadratic RBFs are used. These schemes enhance the local accuracy and convergence by locally optimizing the shape parameters. Comparing with the original WENO with Lax–Wendroff time discretization schemes of Qiu for HJ equations, the new schemes provide more accurate reconstructions and sharper solution profiles near strong discontinuous derivative. Also, the RENO/RWENO‐LW schemes are easy to implement in the existing original ENO/WENO code. Extensive numerical experiments are considered to verify the capability of the new schemes. |
| doi_str_mv | 10.1002/num.22542 |
| format | Article |
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Particularly the multi‐quadratic RBFs are used. These schemes enhance the local accuracy and convergence by locally optimizing the shape parameters. Comparing with the original WENO with Lax–Wendroff time discretization schemes of Qiu for HJ equations, the new schemes provide more accurate reconstructions and sharper solution profiles near strong discontinuous derivative. Also, the RENO/RWENO‐LW schemes are easy to implement in the existing original ENO/WENO code. 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Extensive numerical experiments are considered to verify the capability of the new schemes.</description><subject>Discretization</subject><subject>finite difference method</subject><subject>Hamilton–Jacobi equations</subject><subject>Lax–Wendroff type time discretization</subject><subject>Radial basis function</subject><subject>radial basis functions interpolation</subject><subject>RBF‐ENO/WENO scheme</subject><issn>0749-159X</issn><issn>1098-2426</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kLFOwzAQhi0EEqUw8AaWmBjS2o6T2CNUlIJKKyGqslkmOauumqS1E5Uy9RGQeMM-CYGwstw_3PffSR9Cl5T0KCGsX9R5j7GIsyPUoUSKgHEWH6MOSbgMaCRfT9GZ90tCKI2o7KDs-XZ42H_eTab9eTOwTxeQg8dbWy3wWL8f9l9zKDJXGoOr3RpwZXPAmfWpg8p-6MqWhcemdHikc7uqyqJpPOq0fLMYNnW7P0cnRq88XPxlF82Gdy-DUTCe3j8MbsZByihjAacSTEIACE0iwzQNRZgIQ3mqiZFCiBgkD00Yc8IhyVIOMtOMhUQTECJjYRddtXfXrtzU4Cu1LGtXNC8V43FIacyisKGuWyp1pfcOjFo7m2u3U5SoH4mqkah-JTZsv2W3dgW7_0E1mT21jW_nZHXH</recordid><startdate>202101</startdate><enddate>202101</enddate><creator>Abedian, Rooholah</creator><creator>Dehghan, Mehdi</creator><general>John Wiley & Sons, Inc</general><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-2573-9755</orcidid><orcidid>https://orcid.org/0000-0002-1739-5964</orcidid></search><sort><creationdate>202101</creationdate><title>RBF‐ENO/WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations</title><author>Abedian, Rooholah ; Dehghan, Mehdi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2122-419ef70ee0175f2a138378f14ca0f98886e943f36404e7dc4e9da2230a0e88d23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Discretization</topic><topic>finite difference method</topic><topic>Hamilton–Jacobi equations</topic><topic>Lax–Wendroff type time discretization</topic><topic>Radial basis function</topic><topic>radial basis functions interpolation</topic><topic>RBF‐ENO/WENO scheme</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Abedian, Rooholah</creatorcontrib><creatorcontrib>Dehghan, Mehdi</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Numerical methods for partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Abedian, Rooholah</au><au>Dehghan, Mehdi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>RBF‐ENO/WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations</atitle><jtitle>Numerical methods for partial differential equations</jtitle><date>2021-01</date><risdate>2021</risdate><volume>37</volume><issue>1</issue><spage>594</spage><epage>613</epage><pages>594-613</pages><issn>0749-159X</issn><eissn>1098-2426</eissn><abstract>In this research, a class of radial basis functions (RBFs) ENO/WENO schemes with a Lax–Wendroff time discretization procedure, named as RENO/RWENO‐LW, for solving Hamilton–Jacobi (H–J) equations is designed. 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| subjects | Discretization finite difference method Hamilton–Jacobi equations Lax–Wendroff type time discretization Radial basis function radial basis functions interpolation RBF‐ENO/WENO scheme |
| title | RBF‐ENO/WENO schemes with Lax–Wendroff type time discretizations for Hamilton–Jacobi equations |
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