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Efficient Spectral Collocation Method for Tempered Fractional Differential Equations
Fractal and Fractional, 2023 Transient anomalous diffusion may be modeled by a tempered fractional diffusion equation. In this paper, we present a spectral collocation method with tempered fractional Jacobi functions (TFJFs) as basis functions and obtain an efficient algorithm to ...
Tinggang Zhao
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Spectral collocation method for convection-diffusion equation
Demonstratio MathematicaSpectral collocation method, named linear barycentric rational interpolation collocation method (LBRICM), for convection-diffusion (C-D) equation with constant coefficient is considered.
Li Jin, Cheng Yongling
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Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations [PDF]
Advances in Mathematical Physics, 2013 We propose and analyze a spectral Jacobi-collocation approximation for fractional order integrodifferential equations of Volterra type with pantograph delay. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis
Yin Yang, Yunqing Huang
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Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method [PDF]
Abstract and Applied Analysis, 2014 The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method.
Peyman Hessari +2 more
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A collocation spectral method for two-dimensional Sobolev equations
Boundary Value Problems, 2018 This article mainly studies a collocation spectral method for two-dimensional (2D) Sobolev equations. To this end, a collocation spectral model based on the Chebyshev polynomials for the 2D Sobolev equations is first established. And then, the existence,
Shiju Jin, Zhendong Luo
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A Crank–Nicolson collocation spectral method for the two-dimensional telegraph equations
Journal of Inequalities and Applications, 2018 In this paper, we mainly focus to study the Crank–Nicolson collocation spectral method for two-dimensional (2D) telegraph equations. For this purpose, we first establish a Crank–Nicolson collocation spectral model based on the Chebyshev polynomials for ...
Yanjie Zhou, Zhendong Luo
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A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem [PDF]
ESAIM: Mathematical Modelling and Numerical Analysis, 2002 A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of ...
Andreas Karageorghis, Bernard Bialecki
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Nonlinear Engineering, 2020 In this work, we present a new modification to the bivariate spectral collocation method in solving Emden-Fowler equations. The novelty of the modified approach is the use of overlapping grids when applying the Chebyshev spectral collocation method.
Mkhatshwa Musawenkhosi P. +2 more
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Domain decomposition preconditioners for the spectral collocation method [PDF]
Journal of Scientific Computing, 1988 Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles.
Quarteroni, Alfio +3 more
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Journal of Mathematical Analysis and Applications, 2007 In this study, we use the spectral collocation method with preconditioning to solve various nonlinear Schrödinger equations. To reduce round-off error in spectral collocation method we use preconditioning.
Javidi, M., Golbabai, A.
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