Use of Green's functions in the numerical solution of two-point boundary value problems
This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and...
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| creator | Gallaher, L. J. Perlin, I. E. |
| description | This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system. |
| doi_str_mv | 10.1007/BFb0066602 |
| format | Book Chapter |
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E.</creator><contributor>Bettis, Dale G.</contributor><creatorcontrib>Gallaher, L. J. ; Perlin, I. E. ; Bettis, Dale G.</creatorcontrib><description>This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. 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Examples here include some problems in finding rendezvous orbits of the restricted three body system.</description><subject>Iterative Scheme</subject><subject>Local Convergence Theorem</subject><subject>Order Linear Ordinary Differential Equation</subject><subject>Order Ordinary Differential Equation</subject><subject>Relaxation Parameter</subject><issn>0075-8434</issn><issn>1617-9692</issn><isbn>9783540066026</isbn><isbn>3540066020</isbn><isbn>9783540379119</isbn><isbn>3540379118</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2006</creationdate><recordtype>book_chapter</recordtype><sourceid/><recordid>eNqVj71OxDAQhM2fRARpeILtoAms48SJWxAHD8Dpyig5HDD4vJE3BvH2XCQENdNMMd8UnxAXEq8lYnNzuxoQtdZYHojcNK2qK1SNkdIcikxq2RRGm_Lod8MF1cci25_roq1UdSpy5jfcR5V121aZ2KzZAo3wEK0NlwxjCtvZUWBwAeZXCyHtbHTb3gOTT8u04PMnFRO5MMNAKTz38Qs-ep8sTJEGb3d8Lk7G3rPNf_pMXK3un-4eC56iCy82dgPRO3cSu8Wt-3NT_0C_AecNTqs</recordid><startdate>20060827</startdate><enddate>20060827</enddate><creator>Gallaher, L. J.</creator><creator>Perlin, I. E.</creator><general>Springer Berlin Heidelberg</general><scope/></search><sort><creationdate>20060827</creationdate><title>Use of Green's functions in the numerical solution of two-point boundary value problems</title><author>Gallaher, L. J. ; Perlin, I. E.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-springer_books_10_1007_BFb00666023</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Iterative Scheme</topic><topic>Local Convergence Theorem</topic><topic>Order Linear Ordinary Differential Equation</topic><topic>Order Ordinary Differential Equation</topic><topic>Relaxation Parameter</topic><toplevel>online_resources</toplevel><creatorcontrib>Gallaher, L. J.</creatorcontrib><creatorcontrib>Perlin, I. E.</creatorcontrib></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gallaher, L. J.</au><au>Perlin, I. E.</au><au>Bettis, Dale G.</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Use of Green's functions in the numerical solution of two-point boundary value problems</atitle><btitle>Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations</btitle><seriestitle>Lecture Notes in Mathematics</seriestitle><date>2006-08-27</date><risdate>2006</risdate><spage>374</spage><epage>407</epage><pages>374-407</pages><issn>0075-8434</issn><eissn>1617-9692</eissn><isbn>9783540066026</isbn><isbn>3540066020</isbn><eisbn>9783540379119</eisbn><eisbn>3540379118</eisbn><abstract>This study investigates the use of Green's functions in the numerical solution of the two-point boundary value problem. The first part deals with the role of the Green's function in solving both linear and nonlinear second order ordinary differential equations with boundary conditions and systems of such equations. The second part describes procedures for numerical construction of Green's functions and considers briefly the conditions for their existence. Finally, there is a description of some numerical experiments using nonlinear problems for which the known existence, uniqueness or convergence theorems do not apply. Examples here include some problems in finding rendezvous orbits of the restricted three body system.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/BFb0066602</doi></addata></record> |
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| ispartof | Proceedings of the Conference on the Numerical Solution of Ordinary Differential Equations, 2006, p.374-407 |
| issn | 0075-8434 1617-9692 |
| language | eng |
| recordid | cdi_springer_books_10_1007_BFb0066602 |
| source | Springer Books |
| subjects | Iterative Scheme Local Convergence Theorem Order Linear Ordinary Differential Equation Order Ordinary Differential Equation Relaxation Parameter |
| title | Use of Green's functions in the numerical solution of two-point boundary value problems |
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