Symmetric and symplectic exponentially fitted Runge–Kutta methods of high order
The construction of high order symmetric, symplectic and exponentially fitted Runge–Kutta (RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is analyzed. Based on the symplecticness, symmetry, and exponential fitting properties, three new four-stage RK integ...
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| Veröffentlicht in: | Computer physics communications 2010-12, Vol.181 (12), p.2044-2056 |
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| container_title | Computer physics communications |
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| creator | Calvo, M. Franco, J.M. Montijano, J.I. Rández, L. |
| description | The construction of high order symmetric, symplectic and exponentially fitted Runge–Kutta (RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is analyzed. Based on the symplecticness, symmetry, and exponential fitting properties, three new four-stage RK integrators, either with fixed- or variable-nodes, are constructed. The algebraic order of the new integrators is also studied, showing that they possess eighth-order of accuracy as the classical four-stage RK Gauss method. Numerical experiments with some oscillatory test problems are presented to show that the new methods are more efficient than other symplectic four-stage eighth-order RK Gauss codes proposed in the scientific literature. |
| doi_str_mv | 10.1016/j.cpc.2010.08.019 |
| format | Article |
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Numerical experiments with some oscillatory test problems are presented to show that the new methods are more efficient than other symplectic four-stage eighth-order RK Gauss codes proposed in the scientific literature.</description><subject>Algebra</subject><subject>Computer simulation</subject><subject>Construction</subject><subject>Exponential fitting</subject><subject>Fittings</subject><subject>Integrators</subject><subject>Mathematical models</subject><subject>Oscillatory Hamiltonian systems</subject><subject>Runge-Kutta method</subject><subject>Runge–Kutta methods</subject><subject>Symmetry</subject><subject>Symplecticness</subject><issn>0010-4655</issn><issn>1879-2944</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwAey8g02CHTsPixWqeIlKiNfaSuxJ6yovbAeRHf_AH_IlGJV1NzO6mntnNAehU0piSmh2sYnVoOKEBE2KmFCxh2a0yEWUCM730YyEScSzND1ER85tCCF5LtgMPb1MbQveGoXLTmM3tUMDygcJn0PfQedN2TQTro33oPHz2K3g5-v7YfS-xCG47rXDfY3XZrXGvdVgj9FBXTYOTv77HL3dXL8u7qLl4-394moZKZ4UPqpyBqJWVcIFcF5zDmlWJpUqEqIhrXhOWE0SmjLNVB0qKKZ0mqiM0qwinLE5OtvuHWz_PoLzsjVOQdOUHfSjkwWjVLBUZMF5vtNJ83CMUcJFsNKtVdneOQu1HKxpSztJSuQfaLmRAbT8Ay1JIQPokLncZiB8-2HASqcMdAq0sQGl1L3Zkf4FhUKHXg</recordid><startdate>20101201</startdate><enddate>20101201</enddate><creator>Calvo, M.</creator><creator>Franco, J.M.</creator><creator>Montijano, J.I.</creator><creator>Rández, L.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20101201</creationdate><title>Symmetric and symplectic exponentially fitted Runge–Kutta methods of high order</title><author>Calvo, M. ; Franco, J.M. ; Montijano, J.I. ; Rández, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c428t-b73e9fcb249e44f44e56a2bc820de5b4703f02153d3cf53dec3cd52c6116b0433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Computer simulation</topic><topic>Construction</topic><topic>Exponential fitting</topic><topic>Fittings</topic><topic>Integrators</topic><topic>Mathematical models</topic><topic>Oscillatory Hamiltonian systems</topic><topic>Runge-Kutta method</topic><topic>Runge–Kutta methods</topic><topic>Symmetry</topic><topic>Symplecticness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Calvo, M.</creatorcontrib><creatorcontrib>Franco, J.M.</creatorcontrib><creatorcontrib>Montijano, J.I.</creatorcontrib><creatorcontrib>Rández, L.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</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>Computer physics communications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Calvo, M.</au><au>Franco, J.M.</au><au>Montijano, J.I.</au><au>Rández, L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Symmetric and symplectic exponentially fitted Runge–Kutta methods of high order</atitle><jtitle>Computer physics communications</jtitle><date>2010-12-01</date><risdate>2010</risdate><volume>181</volume><issue>12</issue><spage>2044</spage><epage>2056</epage><pages>2044-2056</pages><issn>0010-4655</issn><eissn>1879-2944</eissn><abstract>The construction of high order symmetric, symplectic and exponentially fitted Runge–Kutta (RK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is analyzed. 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| issn | 0010-4655 1879-2944 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Algebra Computer simulation Construction Exponential fitting Fittings Integrators Mathematical models Oscillatory Hamiltonian systems Runge-Kutta method Runge–Kutta methods Symmetry Symplecticness |
| title | Symmetric and symplectic exponentially fitted Runge–Kutta methods of high order |
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