High‐order compact schemes for fractional differential equations with mixed derivatives

Vong, Seakweng; Shi, Chenyang; Lyu, Pin

doi:10.1002/num.22183

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…For simplicity, in this paper we restrict ourselves to the case of a uniform mesh, and assume the smoothness of the solution. Other related works include, but not limited to [2,8,38]. In principle, these methods can be directly generalized to nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

Cai¹

2021

NMTMA

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We introduce a high-order numerical scheme for fractional ordinary differential equations with the Caputo derivative. The method is developed by dividing the domain into a number of subintervals, and applying the quadratic interpolation on each subinterval. The method is shown to be unconditionally stable, and for general nonlinear equations, the uniform sharp numerical order 3 − ν can be rigorously proven for sufficiently smooth solutions at all time steps. The proof provides a general guide for proving the sharp order for higher-order schemes in the nonlinear case. Some numerical examples are given to validate our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

Cai¹

2021

NMTMA

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A variable‐step high‐order scheme for time‐fractional advection‐diffusion equation with mixed derivatives

Feng,

Lyu,

Vong

2024

Numerical Methods Partial

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We consider a high accuracy numerical scheme for solving the two‐dimensional time‐fractional advection‐diffusion equation including mixed derivatives, where the variable‐step Alikhanov formula and a fourth‐order compact approximation are employed to time and space derivatives, respectively. Under mild assumptions on the time step‐sizes, we obtain the unconditional stability and high‐order convergence (second‐order in time and fourth‐order in space) of the proposed scheme by energy method. The theoretical statements are justified by the numerical experiments.

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A Compact Difference Scheme for Fourth-Order Fractional Sub-Diffusion Equations With Neumann Boundary Conditions

Yao¹,

Wang²

2018

jaac

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High‐order compact schemes for fractional differential equations with mixed derivatives

Cited by 4 publications

References 32 publications

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy

A variable‐step high‐order scheme for time‐fractional advection‐diffusion equation with mixed derivatives

A Compact Difference Scheme for Fourth-Order Fractional Sub-Diffusion Equations With Neumann Boundary Conditions

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