Some temporal second order difference schemes for fractional wave equations (Q2808872)
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scientific article; zbMATH DE number 6584627
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some temporal second order difference schemes for fractional wave equations |
scientific article; zbMATH DE number 6584627 |
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Some temporal second order difference schemes for fractional wave equations (English)
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25 May 2016
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convergence
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finite difference scheme
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fractional wave equation
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stability
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discrete energy method
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numerical examples
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0.9678791
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0.9570167
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Finite difference schemes are proposed for the numerical solution of the fractional wave equation. Both the one-dimensional and the two-dimensional problem are considered. The derived schemes are shown to be of second-order accuracy both in time and space. The stability of the schemes in \(H^1\) norm is shown and the convergence is proven with the aid of the discrete energy method. The compact difference scheme in space is presented and analyzed. Moreover, a possible extension to the three-dimensional problem is briefly mentioned. Numerical examples are shown supporting the derived estimates and the efficiency of the proposed schemes.
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