The time discontinuous space-time finite element method for fractional diffusion-wave equation

Zheng, Yuanyuan; Zhao, Zhengang

doi:10.1016/j.apnum.2019.09.007

Cited by 18 publications

(6 citation statements)

References 24 publications

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“…Solusi dari persamaan tersebut diperoleh hanya dengan menggunakan transformasi Laplace, kemudian mengarahkan solusi kedalam bentuk fungsi generalisai Mittag-Leffler [7]. Selain menggunakan teknik transformasi Laplace, permasalahan difusi-gelombang fraksional dapat diselesaikan dengan menggunakan metode diskritisasi seperti pada [8] dan dapat juga diselesaikan dengan metode elemen hingga seperti pada [9]. Penelitian sebelumnya mengkaji difusi-gelombang fraksional pada media yang secara spesifik tidak viskoelastis.…”

Section: Pendahuluanunclassified

Fungsi Wright Sebagai Solusi Analitik Persamaan Difusi-Gelombang Fraksional Pada Media Viskoelastis

Yasa

Gunawan

2020

JFMA

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A fractional diffusion-wave equations in a fractional viscoelastic media can be constructed by using equations of motion and kinematic equations of viscoelasticmaterial in fractional order. This article concerns the fractional diffusion-wave equations in the fractional viscoelastic media for semi-infinite regions that satisfies signalling boundary value problems. Fractional derivative was used in Caputo sense. The analytical solution of the fractional diffusion-wave equation in the fractional viscoelastic media was solved by means of Laplace transform techniques in the term of Wright function for simple form solution. For general parameters, Numerical Inverse Laplace Transforms (NILT) was used to determine the solution.

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Section: Pendahuluanunclassified

Fungsi Wright Sebagai Solusi Analitik Persamaan Difusi-Gelombang Fraksional Pada Media Viskoelastis

Yasa

Gunawan

2020

JFMA

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“…It has been successfully applied to solve some partial differential equations with the integer order (see [23][24][25][26][27][28][29][30][31] for more details). Recently, Mustapha [32], Zheng and Zhao [33], Liu et al [34], Liu et al [35], Bu et al [36], Yue et al [37], and Li et al [38] developed a finite element scheme for the fractional diffusion equation, fractional diffusion wave equation, linear space fractional PDE, nonlinear fractional reaction diffusion system, multi-term time-space fractional diffusion equation, multi-term time fractional advection-diffusion equations, and fractional wave problems, for which the space-time finite element method was adopted.…”

Section: Introductionmentioning

confidence: 99%

A Space-Time Finite Element Method for the Fractional Ginzburg–Landau Equation

Liu

2023

Fractal Fract

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A fully discrete space-time finite element method for the fractional Ginzburg–Landau equation is developed, in which the discontinuous Galerkin finite element scheme is adopted in the temporal direction and the Galerkin finite element scheme is used in the spatial orientation. By taking advantage of the valuable properties of Radau numerical integration and Lagrange interpolation polynomials at the Radau points of each time subinterval In, the well-posedness of the discrete solution is proven. Moreover, the optimal order error estimate in L∞(L2) is also considered in detail. Some numerical examples are provided to evaluate the validity and effectiveness of the theoretical analysis.

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“…Te proposed method was shown to be accurate and efcient for solving this type of equation. In [10], the authors proposed a new approach based on the operational matrix method to solve the space-time fractional difusion equation. Te proposed method was compared with several other numerical methods, and the results showed that it is accurate and efcient.…”

Section: Introductionmentioning

confidence: 99%

A New Method for Solving Sequential Fractional Wave Equations

Syam

Siri

Kasmani

et al. 2023

Journal of Mathematics

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In this article, we focus on two classes of fractional wave equations in the context of the sequential Caputo derivative. For the first class, we derive the closed-form solution in terms of generalized Mittag–Leffler functions. Subsequently, we consider a more general class of nonhomogeneous fractional wave equations. Due to the complexity of finding exact solutions for these problems, we employ a numerical technique based on the operational matrix method to approximate the solution. We provide several theoretical and numerical examples to validate the effectiveness of this numerical approach. The results demonstrate the accuracy and efficiency of the proposed method.

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The time discontinuous space-time finite element method for fractional diffusion-wave equation

Cited by 18 publications

References 24 publications

Fungsi Wright Sebagai Solusi Analitik Persamaan Difusi-Gelombang Fraksional Pada Media Viskoelastis

Fungsi Wright Sebagai Solusi Analitik Persamaan Difusi-Gelombang Fraksional Pada Media Viskoelastis

A Space-Time Finite Element Method for the Fractional Ginzburg–Landau Equation

A New Method for Solving Sequential Fractional Wave Equations

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