Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
2017 ◽
Vol 22
(4)
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pp. 1028-1048
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Keyword(s):
AbstractThe fractional derivatives include nonlocal information and thus their calculation requires huge storage and computational cost for long time simulations. We present an efficient and high-order accurate numerical formula to speed up the evaluation of the Caputo fractional derivative based on theL2-1σformula proposed in [A. Alikhanov,J. Comput. Phys., 280 (2015), pp. 424-438], and employing the sum-of-exponentials approximation to the kernel function appeared in the Caputo fractional derivative. Both theoretically and numerically, we prove that while applied to solving time fractional diffusion equations, our scheme not only has unconditional stability and high accuracy but also reduces the storage and computational cost.
2020 ◽
Vol 80
(5)
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pp. 1443-1458
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2019 ◽
Vol 127
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pp. 158-164
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2019 ◽
Vol 376
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pp. 1312-1330
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2020 ◽
Vol 43
(12)
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pp. 7208-7226
2018 ◽
Vol 373
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pp. 410-424
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Keyword(s):
2017 ◽
Vol 74
(2)
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pp. 1009-1033
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2019 ◽
Vol 137
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pp. 34-48
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