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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1687-9120 1687-9139 |