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• W2945248599 abstract "In present work, a new high-order numerical approximation to the Caputo fractional derivative of order α(0<α<1) is constructed. The quadratic interpolation approximation of Caputo derivative on non-uniform meshes is considered. As a result, the new formula can be viewed as the modification of the existing jobs (Li et al., 2016 [8]; Zhang et al., 2014 [21]). The coefficients and truncation errors are analyzed, then we adopt the derived scheme to solve the fractional diffusion and advection equations with Dirichlet boundary conditions on non-uniform meshes. Moreover, the solvability, unconditional stability and convergence are proved. The effectiveness and accuracy of the scheme is demonstrated by numerical experiments to support the theoretical results." @default.
• W2945248599 created "2019-05-29" @default.
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• W2945248599 date "2019-10-01" @default.
• W2945248599 modified "2023-10-16" @default.
• W2945248599 title "A new approximation to Caputo-type fractional diffusion and advection equations on non-uniform meshes" @default.
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• W2945248599 doi "https://doi.org/10.1016/j.apnum.2019.05.014" @default.
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