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- Author: Borbála Fazekas
- Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
- Year: 2012
- Pages: 152
- ISBN-10: 3838118340
- ISBN-13: 9783838118345
- Format: 15.2 x 22.9 x 0.9 cm, softcover
- Language: English
- SAVE -10% with code: EXTRA
Computer-assisted enclosures for fourth order elliptic equations (e-book) (used book) | bookbook.eu
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"Concerning (partial) differential equations, amongst many others two questions are of great importance: existence and uniqueness, or more general multiplicity of solutions... There are plenty of equations, where analytical methods fail to work." The author describes in this work a computer-assisted method for proving existence and multiplicity of solutions of fourth order nonlinear elliptic boundary value problems. The main idea of this method is to compute a good numerical approximation of a solution and certain defect bounds with computer-assistance. Then a rigorous proof of the existence of an exact solution close to the numerical one is obtained by a fixed-point argument. The efficiency of this method is demonstrated with the examples of the fourth order Gelfand- and Emden-equations on various domains.
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- Author: Borbála Fazekas
- Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
- Year: 2012
- Pages: 152
- ISBN-10: 3838118340
- ISBN-13: 9783838118345
- Format: 15.2 x 22.9 x 0.9 cm, softcover
- Language: English English
"Concerning (partial) differential equations, amongst many others two questions are of great importance: existence and uniqueness, or more general multiplicity of solutions... There are plenty of equations, where analytical methods fail to work." The author describes in this work a computer-assisted method for proving existence and multiplicity of solutions of fourth order nonlinear elliptic boundary value problems. The main idea of this method is to compute a good numerical approximation of a solution and certain defect bounds with computer-assistance. Then a rigorous proof of the existence of an exact solution close to the numerical one is obtained by a fixed-point argument. The efficiency of this method is demonstrated with the examples of the fourth order Gelfand- and Emden-equations on various domains.
Reviews