The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions
This paper presents a method to obtain lower and upper bounds for the minimum distance between points a and b of the solution of the second order linear differential equation y′′+q(x)y=0 satisfying general separated boundary conditions of the type a11y(a)+a12y′(a)=0 and a21y(b)+a22y′(b)=0. The metho...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/126713 |
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| _version_ | 1832555828946665472 |
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| author | Pedro Almenar Lucas Jódar |
| author_facet | Pedro Almenar Lucas Jódar |
| author_sort | Pedro Almenar |
| collection | DOAJ |
| description | This paper presents a method to obtain lower and upper bounds for the minimum distance between points a and b of the solution of the second order linear differential equation y′′+q(x)y=0 satisfying general separated boundary conditions of the type a11y(a)+a12y′(a)=0 and a21y(b)+a22y′(b)=0. The method is based on the recursive application of a linear operator to certain functions, a recursive application that makes these bounds converge to the exact distance between a and b as the recursivity index grows. The method covers conjugacy and disfocality as particular cases. |
| format | Article |
| id | doaj-art-ffd75ae8571941c6aad9b2a392c68a42 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ffd75ae8571941c6aad9b2a392c68a422025-02-03T05:47:14ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/126713126713The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary ConditionsPedro Almenar0Lucas Jódar1Vodafone Central Network and Operations, P. E. Castellana Norte, 28050 Madrid, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera S/N, 46022 Valencia, SpainThis paper presents a method to obtain lower and upper bounds for the minimum distance between points a and b of the solution of the second order linear differential equation y′′+q(x)y=0 satisfying general separated boundary conditions of the type a11y(a)+a12y′(a)=0 and a21y(b)+a22y′(b)=0. The method is based on the recursive application of a linear operator to certain functions, a recursive application that makes these bounds converge to the exact distance between a and b as the recursivity index grows. The method covers conjugacy and disfocality as particular cases.http://dx.doi.org/10.1155/2014/126713 |
| spellingShingle | Pedro Almenar Lucas Jódar The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions Abstract and Applied Analysis |
| title | The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions |
| title_full | The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions |
| title_fullStr | The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions |
| title_full_unstemmed | The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions |
| title_short | The Distance between Points of a Solution of a Second Order Linear Differential Equation Satisfying General Boundary Conditions |
| title_sort | distance between points of a solution of a second order linear differential equation satisfying general boundary conditions |
| url | http://dx.doi.org/10.1155/2014/126713 |
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