The Difference Problem of Obtaining the Parameter of a Parabolic Equation
The boundary value problem of determining the parameter 𝑝 of a parabolic equation 𝜐(𝑡)+𝐴𝜐(𝑡)=𝑓(𝑡)+𝑝(0≤𝑡≤1),𝜐(0)=𝜑,𝜐(1)=𝜓 in an arbitrary Banach space 𝐸 with the strongly positive operator 𝐴 is considered. The first order of accuracy stable difference scheme for the approximate solution of this prob...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/603018 |
| Summary: | The boundary value problem of determining the parameter 𝑝 of a parabolic equation 𝜐(𝑡)+𝐴𝜐(𝑡)=𝑓(𝑡)+𝑝(0≤𝑡≤1),𝜐(0)=𝜑,𝜐(1)=𝜓 in an arbitrary Banach space 𝐸 with the strongly positive operator 𝐴 is considered. The first order of accuracy stable difference scheme for the approximate solution of this problem
is investigated. The well-posedness of this difference scheme is established. Applying the abstract result, the stability and almost coercive stability estimates for the solution of difference schemes for the approximate solution of differential equations with parameter are obtained. |
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| ISSN: | 1085-3375 1687-0409 |