A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications

By Guang‐hua Gao, Zhi‐zhong Sun, Hongwei Zhang. Journal of Computational Physics, 2014

597 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9c0cb6d9c6734db6abf7997eb6427729c8e5f23f

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In Applied Mathematics

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In Numerical Analysis

Citations in the corpus

An approach to construct higher order time discretisation schemes for time fractional partial differential equations with nonsmooth data (2017, background): “1) are sufficiently smooth, for example u ∈ C2[0, T ], there are many time discretisation schemes in the literature, for example, Lubich’s fractional multistep methods [7], [30], [55], [65], [61], [62], [64], the L1 scheme and its modification [28], [26], [18], [29], [47], the spectral method [58] [”
Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, methodology): “For example, the L1-2 scheme due to Gao et al [26] applies a piecewise linear approximation on the first subinterval, and a quadratic approximation on the other subintervals to improve the numerical accuracy.”
A finite difference scheme for the nonlinear time‐fractional partial integro‐differential equation (2020, unknown): “(41) Combining (3) and (41) gives (35).”
High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations (II) (2015, methodology): “In [5], the (3−α)th order scheme was established and used to solve subdiffusion equation without theoretical analysis.”
A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems (2018, methodology): “There are other practically important formulas, such as the Caputo BDF2-like approach [7, 13, 18].”
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations (2015, unknown): “There are also high-order discretization scheme by using piecewise high-order polynomial interpolation of u [9, 20, 35, 46].”
A new difference scheme for the time fractional diffusion equation (2014, unknown): “If the stability and convergence of diﬀerence schemes from [22] will be strictly proved, then this will undoubtedly be a signiﬁcant progress in computing the time-fractional partial diﬀerential equations.”