Finite difference methods for computing eigenvalues of fourth order boundary value problems
This brief report describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation y(4)+(p(x)−λq(x))y=0. These methods are derived from the formulah4y1(4)=(δ4−16δ6+7240δ8−…)yi.Num...
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| Format: | Article |
| Language: | English |
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Wiley
1986-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171286000170 |
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| _version_ | 1849397089581137920 |
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| author | Riaz A. Usmani |
| author_facet | Riaz A. Usmani |
| author_sort | Riaz A. Usmani |
| collection | DOAJ |
| description | This brief report describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation y(4)+(p(x)−λq(x))y=0. These methods are derived from the formulah4y1(4)=(δ4−16δ6+7240δ8−…)yi.Numerical results are included to demonstrate practical usefulness of our methods. |
| format | Article |
| id | doaj-art-a8cfd9739c234d8a9972d2e49b4e0f29 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1986-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-a8cfd9739c234d8a9972d2e49b4e0f292025-08-20T03:39:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251986-01-019113714310.1155/S0161171286000170Finite difference methods for computing eigenvalues of fourth order boundary value problemsRiaz A. Usmani0Department of Applied Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, CanadaThis brief report describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two point boundary value problem associated with a fourth order linear differential equation y(4)+(p(x)−λq(x))y=0. These methods are derived from the formulah4y1(4)=(δ4−16δ6+7240δ8−…)yi.Numerical results are included to demonstrate practical usefulness of our methods.http://dx.doi.org/10.1155/S0161171286000170central difference formulafinite difference methodsgeneralized symmetric eigenvalue problempositive definite matrixtwo-point boundary value problem. |
| spellingShingle | Riaz A. Usmani Finite difference methods for computing eigenvalues of fourth order boundary value problems International Journal of Mathematics and Mathematical Sciences central difference formula finite difference methods generalized symmetric eigenvalue problem positive definite matrix two-point boundary value problem. |
| title | Finite difference methods for computing eigenvalues of fourth order boundary value problems |
| title_full | Finite difference methods for computing eigenvalues of fourth order boundary value problems |
| title_fullStr | Finite difference methods for computing eigenvalues of fourth order boundary value problems |
| title_full_unstemmed | Finite difference methods for computing eigenvalues of fourth order boundary value problems |
| title_short | Finite difference methods for computing eigenvalues of fourth order boundary value problems |
| title_sort | finite difference methods for computing eigenvalues of fourth order boundary value problems |
| topic | central difference formula finite difference methods generalized symmetric eigenvalue problem positive definite matrix two-point boundary value problem. |
| url | http://dx.doi.org/10.1155/S0161171286000170 |
| work_keys_str_mv | AT riazausmani finitedifferencemethodsforcomputingeigenvaluesoffourthorderboundaryvalueproblems |