A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation

Wenhui, Guan; Cao, Xuenian

doi:10.1007/s42967-020-00080-8

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…and its definition is [35]. Compared to the ordinary Caputo FSDEs, the CTFSDEs can describe some stochastic phenomena that the first moment of the waiting time of a particle is unbounded [36]. The goal of this work is that we firstly prove the well-posedness of the solution of the above multi-term CTFSDEs, and then construct a EM method for numerically solving it and analyze the strong convergence of this derived EM method.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

Huang,

Shao,

Liu

2024

Phys. Scr.

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In this paper, we first prove the existence, uniqueness and continuity dependence on the initial value of multi-term Caputo tempered fractional stochastic differential equations with initial value. Then, an Euler-Maruyama (EM) method is presented for solving the considered equation. The strong convergence of the presented EM method is strictly investigated with the order to be $\min\{\alpha_m-\alpha_{m-1},\alpha_{m}-0.5\}$ with $0<\alpha_{1}<\alpha_{2}<\cdots<\alpha_{m-1}<\alpha_{m}<1$, $\alpha_{m}>0.5$, and $m$ is a given positive integer. Finally, three numerical examples are provided to support our theoretical findings.

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Section: Introductionmentioning

confidence: 99%

Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

Huang,

Shao,

Liu

2024

Phys. Scr.

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High-order spectral collocation method using tempered fractional Sturm–Liouville eigenproblems

Dahy,

El-Hawary,

Fahim

et al. 2023

Comp. Appl. Math.

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This paper presents an accurate exponential tempered fractional spectral collocation method (TFSCM) to solve one-dimensional and time-dependent tempered fractional partial differential equations (TFPDEs). We use a family of tempered fractional Sturm–Liouville eigenproblems (TFSLP) as a basis and the fractional Lagrange interpolants (FLIs) that generally satisfy the Kronecker delta (KD) function at the employed collocation points. Firstly, we drive the corresponding tempered fractional differentiation matrices (TFDMs). Then, we treat with various linear and nonlinear TFPDEs, among them, the space-tempered fractional advection and diffusion problem, the time-space tempered fractional advection–diffusion problem (TFADP), the multi-term time-space tempered fractional problems, and the time-space tempered fractional Burgers’ equation (TFBE) to investigate the numerical capability of the fractional collocation method. The study includes a numerical examination of the produced condition number $$\kappa (A)$$ κ ( A ) of the linear systems. The accuracy and efficiency of the proposed method are studied from the standpoint of the $$L^\infty $$ L ∞ -norm error and exponential rate of spectral convergence.

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2-D Modeling and Analysis of Time-Domain Electromagnetic Anomalous Diffusion With Space-Fractional Derivative

Gao

Zhao

et al. 2023

IEEE Trans. Geosci. Remote Sensing

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A Numerical Algorithm for the Caputo Tempered Fractional Advection-Diffusion Equation

Cited by 3 publications

References 25 publications

Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

Well-posedness and an Euler-Maruyama method for multi-term caputo tempered fractional stochastic differential equations

High-order spectral collocation method using tempered fractional Sturm–Liouville eigenproblems

2-D Modeling and Analysis of Time-Domain Electromagnetic Anomalous Diffusion With Space-Fractional Derivative

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