Generalized quasilinearization method and higher order of convergence for second-order boundary value problems
<p>The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of <mml:math alttext="$2$"> <mml:mn>2</mml:mn> </mml:math>-hyperconvex and <mml:math alttext="$2$">...
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2006-01-01
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| Series: | Boundary Value Problems |
| Online Access: | http://www.hindawi.com/GetArticle.aspx?doi=10.1155/BVP/2006/25715 |
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doaj-65901b70dcec475d86701a85afa15ad52020-11-25T02:33:36ZengSpringerOpenBoundary Value Problems1687-27622006-01-012006Generalized quasilinearization method and higher order of convergence for second-order boundary value problems<p>The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of <mml:math alttext="$2$"> <mml:mn>2</mml:mn> </mml:math>-hyperconvex and <mml:math alttext="$2$"> <mml:mn>2</mml:mn> </mml:math>-hyperconcave functions. We develop two sequences under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence is of order <mml:math alttext="$3$"> <mml:mn>3</mml:mn> </mml:math>. Finally, we provide numerical examples to show the application of the generalized quasilinearization method developed here for second-order boundary value problems.</p>http://www.hindawi.com/GetArticle.aspx?doi=10.1155/BVP/2006/25715 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| title |
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems |
| spellingShingle |
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems Boundary Value Problems |
| title_short |
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems |
| title_full |
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems |
| title_fullStr |
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems |
| title_full_unstemmed |
Generalized quasilinearization method and higher order of convergence for second-order boundary value problems |
| title_sort |
generalized quasilinearization method and higher order of convergence for second-order boundary value problems |
| publisher |
SpringerOpen |
| series |
Boundary Value Problems |
| issn |
1687-2762 |
| publishDate |
2006-01-01 |
| description |
<p>The method of generalized quasilinearization for second-order boundary value problems has been extended when the forcing function is the sum of <mml:math alttext="$2$"> <mml:mn>2</mml:mn> </mml:math>-hyperconvex and <mml:math alttext="$2$"> <mml:mn>2</mml:mn> </mml:math>-hyperconcave functions. We develop two sequences under suitable conditions which converge to the unique solution of the boundary value problem. Furthermore, the convergence is of order <mml:math alttext="$3$"> <mml:mn>3</mml:mn> </mml:math>. Finally, we provide numerical examples to show the application of the generalized quasilinearization method developed here for second-order boundary value problems.</p> |
| url |
http://www.hindawi.com/GetArticle.aspx?doi=10.1155/BVP/2006/25715 |
| _version_ |
1724812853563621376 |