Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients
A complete family of solutions for the one-dimensional reaction-diffusion equation, uxx(x,t)-q(x)u(x,t)=ut(x,t), with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/2947275 |
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| author | Vladislav V. Kravchenko Josafath A. Otero Sergii M. Torba |
| author_facet | Vladislav V. Kravchenko Josafath A. Otero Sergii M. Torba |
| author_sort | Vladislav V. Kravchenko |
| collection | DOAJ |
| description | A complete family of solutions for the one-dimensional reaction-diffusion equation, uxx(x,t)-q(x)u(x,t)=ut(x,t), with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper, the Dirichlet boundary conditions are considered; however, the proposed method can be easily extended onto other standard boundary conditions. The proposed numerical method is shown to reveal good accuracy. |
| format | Article |
| id | doaj-art-9d054038acdd45519d6685dba8eaee2c |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9d054038acdd45519d6685dba8eaee2c2025-02-03T01:07:58ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/29472752947275Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable CoefficientsVladislav V. Kravchenko0Josafath A. Otero1Sergii M. Torba2Departamento de Matemáticas, Unidad Querétaro, CINVESTAV del IPN, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, 76230 Querétaro, QRO, MexicoDepartamento de Matemáticas, Unidad Querétaro, CINVESTAV del IPN, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, 76230 Querétaro, QRO, MexicoDepartamento de Matemáticas, Unidad Querétaro, CINVESTAV del IPN, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, 76230 Querétaro, QRO, MexicoA complete family of solutions for the one-dimensional reaction-diffusion equation, uxx(x,t)-q(x)u(x,t)=ut(x,t), with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper, the Dirichlet boundary conditions are considered; however, the proposed method can be easily extended onto other standard boundary conditions. The proposed numerical method is shown to reveal good accuracy.http://dx.doi.org/10.1155/2017/2947275 |
| spellingShingle | Vladislav V. Kravchenko Josafath A. Otero Sergii M. Torba Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients Advances in Mathematical Physics |
| title | Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients |
| title_full | Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients |
| title_fullStr | Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients |
| title_full_unstemmed | Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients |
| title_short | Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients |
| title_sort | analytic approximation of solutions of parabolic partial differential equations with variable coefficients |
| url | http://dx.doi.org/10.1155/2017/2947275 |
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