Four-step exponential-fitted methods for nonlinear physical problems
We describe a four-step exponential-fitted method for systems of second-order differential equations of the form y″ = ƒ(x,y). This is a sixth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant features are as follows...
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| Veröffentlicht in: | Computer physics communications 1997, Vol.100 (1), p.56-70 |
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| container_title | Computer physics communications |
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| creator | Ixaru, L.Gr Berghe, G.Vanden De Meyer, H. Van Dacle, M. |
| description | We describe a four-step exponential-fitted method for systems of second-order differential equations of the form
y″ = ƒ(x,y). This is a sixth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant features are as follows: (i) it requires only two solution values to start; (ii) it allows modification of the stepsize during the integration process; (iii) it works in the predictor-corrector mode with only one function evaluation per step; (iv) the whole integration process is controlled in terms of the requested value for the local truncation error.
Our method was tested on a representative set of problems taken from physics and found to behave particularly well on the problems involving oscillatory phenomena. A selection of experimental results is given in which our method is compared with a widely used code. |
| doi_str_mv | 10.1016/S0010-4655(96)00147-6 |
| format | Article |
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y″ = ƒ(x,y). This is a sixth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant features are as follows: (i) it requires only two solution values to start; (ii) it allows modification of the stepsize during the integration process; (iii) it works in the predictor-corrector mode with only one function evaluation per step; (iv) the whole integration process is controlled in terms of the requested value for the local truncation error.
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y″ = ƒ(x,y). This is a sixth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant features are as follows: (i) it requires only two solution values to start; (ii) it allows modification of the stepsize during the integration process; (iii) it works in the predictor-corrector mode with only one function evaluation per step; (iv) the whole integration process is controlled in terms of the requested value for the local truncation error.
Our method was tested on a representative set of problems taken from physics and found to behave particularly well on the problems involving oscillatory phenomena. A selection of experimental results is given in which our method is compared with a widely used code.</description><subject>Error control</subject><subject>Exponential fitting</subject><subject>IVP (initial-value problems)</subject><subject>Multistep methods</subject><subject>Predictor-corrector</subject><subject>Stepwise control</subject><subject>Systems of nonlinear second-order ODEs</subject><issn>0010-4655</issn><issn>1879-2944</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1997</creationdate><recordtype>article</recordtype><recordid>eNqFkEFLAzEQhYMoWKs_QdiT6CGaNNmkOYlUq0LBg3oO2eyERnY3a5IV--_dtuLV08zAe294H0LnlFxTQsXNKyGUYC7K8lKJq_HgEosDNKFzqfBMcX6IJn-SY3SS0gchRErFJuh-GYaIU4a-gO8-dNBlbxrsfM5QFy3kdahT4UIsutA1vgMTi369Sd6apuhjqBpo0yk6cqZJcPY7p-h9-fC2eMKrl8fnxd0KW8bmGRvKCXdSEUaZ4Vw6Ala4cYeKCk4szCQtQbjKmMpS6piQzipgFlQlnWRsii72uePjzwFS1q1PFprGdBCGpGeiZFQyNQrLvdDGkFIEp_voWxM3mhK9ZaZ3zPQWiFZC75hpMfpu9z4YW3x5iDpZD52F2kewWdfB_5PwAx-ZdLE</recordid><startdate>1997</startdate><enddate>1997</enddate><creator>Ixaru, L.Gr</creator><creator>Berghe, G.Vanden</creator><creator>De Meyer, H.</creator><creator>Van Dacle, M.</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>1997</creationdate><title>Four-step exponential-fitted methods for nonlinear physical problems</title><author>Ixaru, L.Gr ; Berghe, G.Vanden ; De Meyer, H. ; Van Dacle, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-a1404f790313a447f0ec6f13aeb1640ce2715e6fbaabc11f367fc9e3ce9b7f733</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Error control</topic><topic>Exponential fitting</topic><topic>IVP (initial-value problems)</topic><topic>Multistep methods</topic><topic>Predictor-corrector</topic><topic>Stepwise control</topic><topic>Systems of nonlinear second-order ODEs</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ixaru, L.Gr</creatorcontrib><creatorcontrib>Berghe, G.Vanden</creatorcontrib><creatorcontrib>De Meyer, H.</creatorcontrib><creatorcontrib>Van Dacle, M.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research 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>Ixaru, L.Gr</au><au>Berghe, G.Vanden</au><au>De Meyer, H.</au><au>Van Dacle, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Four-step exponential-fitted methods for nonlinear physical problems</atitle><jtitle>Computer physics communications</jtitle><date>1997</date><risdate>1997</risdate><volume>100</volume><issue>1</issue><spage>56</spage><epage>70</epage><pages>56-70</pages><issn>0010-4655</issn><eissn>1879-2944</eissn><abstract>We describe a four-step exponential-fitted method for systems of second-order differential equations of the form
y″ = ƒ(x,y). This is a sixth-order method depending on five parameters which are automatically adjusted in terms of the equations to be solved. Some other relevant features are as follows: (i) it requires only two solution values to start; (ii) it allows modification of the stepsize during the integration process; (iii) it works in the predictor-corrector mode with only one function evaluation per step; (iv) the whole integration process is controlled in terms of the requested value for the local truncation error.
Our method was tested on a representative set of problems taken from physics and found to behave particularly well on the problems involving oscillatory phenomena. A selection of experimental results is given in which our method is compared with a widely used code.</abstract><pub>Elsevier B.V</pub><doi>10.1016/S0010-4655(96)00147-6</doi><tpages>15</tpages></addata></record> |
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| ispartof | Computer physics communications, 1997, Vol.100 (1), p.56-70 |
| issn | 0010-4655 1879-2944 |
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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Error control Exponential fitting IVP (initial-value problems) Multistep methods Predictor-corrector Stepwise control Systems of nonlinear second-order ODEs |
| title | Four-step exponential-fitted methods for nonlinear physical problems |
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