Results 21 to 30 of about 20,047 (287)
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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ADI-Spectral Collocation Methods for Two-Dimensional Parabolic Equations
East Asian Journal on Applied Mathematics, 2020 Summary: ADI-spectral collocation methods for two-dimensional parabolic equations on bounded and unbounded domains are studied. A spectral collocation scheme is adopted for spatial discretisation and the Crank-Nicolson ADI scheme is used for time discretisation.
Gu, Dong-Qin +2 more
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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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Optimal Collocation Nodes for Fractional Derivative Operators [PDF]
, 2014 Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the function to be
Fatone, Lorella, Funaro, Daniele
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Polynomial spectral collocation method for space fractional advection–diffusion equation [PDF]
Numerical Methods for Partial Differential Equations, 2013 This article discusses the spectral collocation method for numerically solving nonlocal problems: one‐dimensional space fractional advection–diffusion equation; and two‐dimensional linear/nonlinear space fractional advection–diffusion equation. The differentiation matrixes of the left and right Riemann–Liouville and Caputo fractional derivatives are ...
Tian, WenYi, Deng, Weihua, Wu, Yujiang
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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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Journal of Function Spaces, 2021 In this paper, the Crank-Nicolson Fourier spectral method is proposed for solving the space fractional Schrödinger equation with wave operators. The equation is treated with the conserved Crank-Nicolson Fourier Galerkin method and the conserved Crank ...
Lei Zhang +3 more
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Open Physics, 2020 The present study aims to design a second-order nonlinear Lane–Emden coupled functional differential model and numerically investigate by using the famous spectral collocation method.
Abdelkawy Mohamed A. +3 more
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On the bivariate spectral quasi-linearization method for solving the two-dimensional Bratu problem
Open Physics, 2018 In this paper, a bivariate spectral quasi-linearization method is used to solve the highly non-linear two dimensional Bratu problem. The two dimensional Bratu problem is also solved using the Chebyshev spectral collocation method which uses Kronecker ...
Muzara Hillary +2 more
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Fractal and Fractional, 2023 This work presents a highly accurate method for the numerical solution of the advection–diffusion equation of fractional order. In our proposed method, we apply the Laplace transform to handle the time-fractional derivative and utilize the Chebyshev ...
Farman Ali Shah +4 more
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