Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing
This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to ha...
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| Published in | Mathematical problems in engineering Vol. 2015; no. 2015; pp. 1 - 9 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
01.01.2015
John Wiley & Sons, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1024-123X 1563-5147 |
| DOI | 10.1155/2015/573932 |
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| Abstract | This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems. |
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| AbstractList | This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems. |
| Author | Ji, Wen Wu, Boying Rho, Seungmin Zhou, Guanglu |
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| Copyright | Copyright © 2015 Guanglu Zhou et al. Copyright © 2015 Guanglu Zhou et al. Guanglu Zhou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. |
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| SubjectTerms | Approximation Biological computing Boundary conditions Coefficients Equivalence Exact solutions Inverse problems Iterative methods Lagrange multiplier Mathematical analysis Mathematical models Mathematical problems Methods Nonlinear equations Numerical analysis Parabolic differential equations Partial differential equations Sensor arrays Time dependence Time measurement |
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| Title | Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing |
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