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Two Weighted Average Finite Difference Schemes for Variable-Order Fractional Mixed Diffusion and Diffusion-Wave Equation |
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PP: 677-689 |
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doi:10.18576/pfda/110404
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Author(s) |
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Nasser. H. Sweilam,
Adel.A. Darwish,
Nada Henidy,
Salma A. Shatta,
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Abstract |
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| In this paper is investigated variable-order mixed diffusion and diffusion-wave model problems. The variable-order derivatives are formulated using the Caputo definition. For the numerical computation of these equations in one and two dimensions, we propose two weighted average finite difference methods: a nonstandard and a standard approach. We further analyze the stability and truncation error of these schemes. Numerical experiments illustrate the memory properties of the proposed methods and establish their computational effectiveness and numerical accuracy. The results confirm that the proposed methods efficiently solve variable-order equations. |
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