On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems
A second order of accuracy difference scheme for the approximate solution of the abstract nonlocal boundary value problem −d2u(t)/dt2+Au(t)=g(t), (0≤t≤1), du(t)/dt−Au(t)=f(t), (−1≤t≤0), u(1)=u(−1)+μ for differential equations in a Hilbert space H with a self-adjoint positive definite operator A is c...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/705172 |
| Summary: | A second order of accuracy difference
scheme for the approximate solution of the abstract nonlocal boundary value
problem −d2u(t)/dt2+Au(t)=g(t), (0≤t≤1), du(t)/dt−Au(t)=f(t), (−1≤t≤0), u(1)=u(−1)+μ for differential equations in a Hilbert space H with a self-adjoint positive definite
operator A is considered. The well posedness of this difference scheme in Hölder
spaces is established. In applications, coercivity inequalities for the solution of a
difference scheme for elliptic-parabolic equations are obtained and a numerical
example is presented. |
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| ISSN: | 1085-3375 1687-0409 |