Numerical solution via Laplace transforms of a fractional order evolution equation (Q973894)
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scientific article; zbMATH DE number 5712447
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Numerical solution via Laplace transforms of a fractional order evolution equation |
scientific article; zbMATH DE number 5712447 |
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Numerical solution via Laplace transforms of a fractional order evolution equation (English)
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26 May 2010
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The authors discuss the integration of a fractional-order diffusion or wave equation with respect to the time variable. The approach is based on the Laplace transform combined with a highly accurate numerical quadrature formula. Three different quadrature formulas are introduced and their convergence properties are studied in detail. Finally, a fully discrete method is constructed based on the schemes introduced above for the time integration and a finite element method for the space variables.
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fractional order diffusion equation
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Laplace transformation
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resolvent
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quadrature
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spatially semidiscrete approximation
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finite elements
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fractional order wave equation
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quadrature formula
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convergence
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