Results 21 to 30 of about 21,259 (289)
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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Alexandria Engineering Journal, 2022 Investigation of spectral (collocation or Galerkin) methods for the solution approximation of different classes of optimal control problems have had been increased in recent years.
Pang Xiaobing +4 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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Chebyshev collocation method for solving second order ODEs using integration matrices
Discrete and Continuous Models and Applied Computational Science, 2023 The spectral collocation method for solving two-point boundary value problems for second order differential equations is implemented, based on representing the solution as an expansion in Chebyshev polynomials. The approach allows a stable calculation of
Konstantin P. Lovetskiy +3 more
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Spectral Methods for Numerical Relativity. The Initial Data Problem [PDF]
, 1999 Numerical relativity has traditionally been pursued via finite differencing. Here we explore pseudospectral collocation (PSC) as an alternative to finite differencing, focusing particularly on the solution of the Hamiltonian constraint (an elliptic ...
Finn, Lee Samuel, Kidder, Lawrence E.
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New recursive approximations for variable-order fractional operators with applications
Mathematical Modelling and Analysis, 2018 To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation.In this paper, we develop Laguerre spectral collocation methods for solving variable-order ...
Mahmoud A. Zaky +3 more
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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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Jacobi Spectral Collocation Technique for Time-Fractional Inverse Heat Equations
Fractal and Fractional, 2021 In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form.
Mohamed A. Abdelkawy +5 more
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A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains [PDF]
, 2009 In this paper, an integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for biharmonic boundary-value ...
Mai-Duy, Nam +2 more
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Fully Legendre spectral collocation technique for stochastic heat equations
Open Physics, 2021 For the stochastic heat equation (SHE), a very accurate spectral method is considered. To solve the SHE, we suggest using a shifted Legendre Gauss–Lobatto collocation approach in combination with a shifted Legendre Gauss–Radau collocation technique.
Abdelkawy Mohamed A. +3 more
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