Method of lines solutions of the parabolic inverse problem with an overspecification at a point
The present work is motivated by the desire to obtain numerical solution to a quasilinear parabolic inverse problem. The solution is presented by means of the method of lines. Method of lines is an alternative computational approach which involves making an approximation to the space derivatives and...
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| Published in | Numerical algorithms Vol. 50; no. 4; pp. 417 - 437 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.04.2009
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1007/s11075-008-9234-3 |
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| Abstract | The present work is motivated by the desire to obtain numerical solution to a quasilinear parabolic inverse problem. The solution is presented by means of the method of lines. Method of lines is an alternative computational approach which involves making an approximation to the space derivatives and reducing the problem to a system of ordinary differential equations in the variable time, then a proper initial value problem solver can be used to solve this ordinary differential equations system. Some numerical examples and also comparison with finite difference methods will be investigated to confirm the efficiency of this procedure. |
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| AbstractList | The present work is motivated by the desire to obtain numerical solution to a quasilinear parabolic inverse problem. The solution is presented by means of the method of lines. Method of lines is an alternative computational approach which involves making an approximation to the space derivatives and reducing the problem to a system of ordinary differential equations in the variable time, then a proper initial value problem solver can be used to solve this ordinary differential equations system. Some numerical examples and also comparison with finite difference methods will be investigated to confirm the efficiency of this procedure. |
| Author | Dehghan, Mehdi Shakeri, Fatemeh |
| Author_xml | – sequence: 1 givenname: Mehdi surname: Dehghan fullname: Dehghan, Mehdi email: mdehghan@aut.ac.ir organization: Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology – sequence: 2 givenname: Fatemeh surname: Shakeri fullname: Shakeri, Fatemeh organization: Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology |
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| Keywords | Overspecified boundary data Method of lines (MOL) Control parameter System of ordinary differential equations (ODEs) Parabolic partial differential equations Inverse problem |
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| SubjectTerms | Algebra Algorithms Approximation Boundary value problems Computer Science Derivatives Differential equations Finite difference method Inverse problems Mathematical analysis Mathematical models Method of lines Numeric Computing Numerical Analysis Original Paper Overspecification Theory of Computation |
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| Title | Method of lines solutions of the parabolic inverse problem with an overspecification at a point |
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