An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion–reaction equations with fixed delay

Zaky, Mahmoud A.; Bockstal, Karel Van; Taha, Thiab R.; Сураган, Дурвудхан; Hendy, Ahmed S.

doi:10.1016/j.cam.2022.114832

Cited by 16 publications

(2 citation statements)

References 59 publications

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“…Fan and Jiang [10] consider an unstructured mesh finite element method for the two-dimensional time-space fractional Schrödinger equation. High-order numerical schemes for time-space fractional differential equations with variable-order fractional derivatives or delay can be found in the work of Zaky et al [11][12][13][14][15]. Furthermore, the L1 Galerkin methods are proposed for the case with nonsmooth solution [16,17].…”

Section: Introductionmentioning

confidence: 99%

L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions

Cai,

2023

Math Methods in App Sciences

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This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain . Here, the temporal partial derivative is in the sense of Caputo with order , and the spatial partial derivatives are of Riesz type with orders in ‐ and ‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples.

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Section: Introductionmentioning

confidence: 99%

L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions

Cai,

2023

Math Methods in App Sciences

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“…Degenerate wave models are gaining more focus these days in many physical applications [6][7][8]. A survey of the numerical techniques that have been applied to direct and inverse problems with integer or fractional order derivatives indicates a lot of focus in recent days [9][10][11]. A reconstruction of missing sole terms in different styles of time-dependent fractional diffusion problems has been seen in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Numerical Reconstruction of a Space-Dependent Reaction Coefficient and Initial Condition for a Multidimensional Wave Equation with Interior Degeneracy

et al. 2023

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A simultaneous reconstruction of the initial condition and the space-dependent reaction coefficient in a multidimensional hyperbolic partial differential equation with interior degeneracy is of concern. A temporal integral observation is utilized to achieve that purpose. The well-posedness, existence, and uniqueness of the inverse problem under consideration are discussed. The inverse problem can be reformulated as a least squares minimization and the Fréchet gradients are determined, using the adjoint and sensitivity problems. Finally, an iterative construction procedure is developed by employing the conjugate gradient algorithm while invoking the discrepancy principle as a stopping criterion. Some numerical experiments are given to ensure the performance of the reconstruction scheme in one and two dimensions.

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Variable-order time-fractional diffusion equation with Mittag-Leffler kernel: regularity analysis and uniqueness of determining variable order

Guo

Zheng

2023

Z. Angew. Math. Phys.

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An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion–reaction equations with fixed delay

Cited by 16 publications

References 59 publications

L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions

L1/LDG algorithm for time‐Caputo space‐Riesz fractional convection equation in two dimensions

Numerical Reconstruction of a Space-Dependent Reaction Coefficient and Initial Condition for a Multidimensional Wave Equation with Interior Degeneracy

Variable-order time-fractional diffusion equation with Mittag-Leffler kernel: regularity analysis and uniqueness of determining variable order

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