A semi-analytical collocation Trefftz scheme for solving multi-term time fractional diffusion-wave equations

Fu, Zhuojia; Yang, Li-Wen; Zhu, Hongping; Xu, Wenzhi

doi:10.1016/j.enganabound.2018.09.017

Cited by 41 publications

(10 citation statements)

References 44 publications

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“…Great attention has been paid to the numerical inversion of the Laplace transformation. General introduction of the Laplace invers was given by Fu et al [34,35,36]. In this paper, the formulations for crack…”

Section: Introductionmentioning

confidence: 99%

Hybrid meshless displacement discontinuity method (MDDM) in fracture mechanics: Static and dynamic

Sládek

et al. 2020

European Journal of Mechanics - A/Solids

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This paper investigated a hybrid Meshless Displacement Discontinuity Method (MDDM) for a cracked plate subjected to static and dynamic loadings. The purpose of MDDM is to model displacement discontinuity on a cracked surface by the displacement discontinuity method in an infinite plate. This was achieved by considering a meshless approach, the equilibrium equations, and the boundary conditions for a domain with an irregular nodes distribution. Also, by imposing the principle of superposition, accurate and convergent solutions can be obtained. In this paper, the static and dynamic stress intensity factors, and the crack growth for different initial crack length and crack slant angles are investigated. The Laplace transform method is applied to deal with dynamic problems and the time-dependent values are obtained by the Durbin inversion technique. Validations of the presented technique are demonstrated by four numerical examples of plates with a central embedded crack.

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Section: Introductionmentioning

confidence: 99%

Hybrid meshless displacement discontinuity method (MDDM) in fracture mechanics: Static and dynamic

Sládek

et al. 2020

European Journal of Mechanics - A/Solids

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“…The modification of the existing finite difference or time integration approaches is one of the most common and dominant computational approaches to deal with time fractional PDEs. [13][14][15]21,22 Recently, Fu et al have proposed and successfully used some approaches based on Laplace transformation 59,60 and spectral collocation Schemes 61 for temporal discretization in the numerical solutions of time fractional PDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of a generalized anomalous electro‐diffusion process in nerve cells by a localized meshless approach in Pseudospectral mode

Ghehsareh

Seidzadeh

Etesami

2020

Int J Numerical Modelling

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Pseudospectral techniques are known as powerful tools and highly accurate solvers to deal with partial differential equations. In the current work, a local meshless technique in Pseudospectral mode is employed to deal with an interesting and general mathematical model which describes anomalous electrodiffusion of ions in spiny dendrites, the two-dimensional variable-order time fractional nonlinear cable equation. For this purpose, at first step a second-order implicit difference method and a modified second-order weighted and shifted Grünwald difference scheme are used to discretize the appearing integer and variable order fractional time derivatives, respectively. Then a local Pseudospectral meshless method based on the sufficiently smooth compactly supported radial point interpolation basis functions is formulated for solving the semidiscretized problem. The main advantage of the proposed computational technique is that it leads to a sparse and better-conditioned system of algebraic equations. Finally, some numerical experiments are presented to demonstrate and verify the performance and accuracy of the method.

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“…The meshless RBF collocation methods have more points of interest and have exhibited superior accuracy as compared with traditional mesh-based numerical methods such as, Finite Difference Method (FDM) [13], Finite Element Method (FEM) [14], Finite Volume Method (FVM) [15][16], and pseudospectral method [17]. For further information [18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…The first derivative from (20) is written as follow From equations (13) and (21) we get the given equation.…”

mentioning

confidence: 99%

Collocation Method for Multiplicative Noise Removal Model

Khan

et al. 2020

Mehran Univ. res. j. eng. technol.

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Image denoising is a fundamental problem in both image processing and computer vision with numerous applications. It can be formulated as an inverse problem. Variational methods are commonly used to solve noise removal problems. The Total Variation (TV) regularization has evolved from an image denoising method for images corrupted with multiplicative noise into a more general technique for inverse problems such as denoising, deblurring, blind deconvolution, and inpainting, which also encompasses the Impulse, Poisson, Speckle, and mixed noise models. Multiplicative noise removal based on TV regularization has been widely researched in image science. In multiplicative noise problems, original image is multiplied by a noise rather than added to the original image. This article proposes a novel meshless collocation technique for the solution of a model having multiplicative noise. This technique includes TV and local collocation along with Multiquadric Radial Basis Function (MQ-RBF) for the solution of associated Euler-Lagrange equation for restoring multiplicative noise from digital images. Numerical examples demonstrate that the proposed algorithm is able to preserve small image details while the noise in the homogeneous regions is removed sufficiently. As a consequence, our method yields better denoised results than those of the current state of the art methods with respect to the Peak-Signal to Noise Ratio (PSNR) values.

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A semi-analytical collocation Trefftz scheme for solving multi-term time fractional diffusion-wave equations

Cited by 41 publications

References 44 publications

Hybrid meshless displacement discontinuity method (MDDM) in fracture mechanics: Static and dynamic

Hybrid meshless displacement discontinuity method (MDDM) in fracture mechanics: Static and dynamic

Numerical simulation of a generalized anomalous electro‐diffusion process in nerve cells by a localized meshless approach in Pseudospectral mode

Collocation Method for Multiplicative Noise Removal Model

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