Implicit difference approximation for the time fractional heat equation with the nonlocal condition (Q651090)
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scientific article; zbMATH DE number 5987761
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Implicit difference approximation for the time fractional heat equation with the nonlocal condition |
scientific article; zbMATH DE number 5987761 |
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Implicit difference approximation for the time fractional heat equation with the nonlocal condition (English)
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8 December 2011
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A time fractional heat equation with a nonlocal condition is considered in a bounded in time and one dimensional space domain. The problem is discretized by approximation of the \(\alpha\)-order Caputo derivative by a first-order weighted finite difference and by a second-order central finite difference for the spatial term. The resulting implicit difference scheme is solved by using a modified Gaussian elimination. The unconditional stability of the method is proved. Numerical examples are given.
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implicit finite difference scheme
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nonlocal fractional parabolic differential equation
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matrix block inversion
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modified Gaussian elimination
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matrix stability
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Kailath theorem
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Schur complement
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time fractional heat equation
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stability
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numerical examples
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