Results 11 to 20 of about 3,143,040 (244)
Advances in Mathematical Physics, 2016 An operational matrix technique is proposed to solve variable order fractional differential-integral equation based on the second kind of Chebyshev polynomials in this paper. The differential operational matrix and integral operational matrix are derived
Jianping Liu, Xia Li, Limeng Wu
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A Mean Square Chain Rule and its Application in Solving the Random Chebyshev Differential Equation
Mediterranean Journal of Mathematics, 2017 In this paper a new version of the chain rule for calculating the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev
J.‐C. Cortés +2 more
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Diffusion Approximation to Neutron Transport Equation with First Kind of Chebyshev Polynomials
Süleyman Demirel Üniversitesi Fen-Edebiyat Fakültesi Fen Dergisi, 2015 : The first kind of Chebyshev polynomials are used for the series expansion of the neutron angular flux in neutron transport theory. The first order approximation known as the diffusion approximation is applied to one-dimensional neutron transport ...
Ökkeş EGE +2 more
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AIMS Mathematics, 2023 In this article, we propose two numerical schemes for solving the time-fractional heat equation (TFHE). The proposed methods are based on applying the collocation and tau spectral methods. We introduce and employ a new set of basis functions: The unified
W. Abd-Elhameed, H. M. Ahmed
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A Spectral Method for Two-Dimensional Ocean Acoustic Propagation
Journal of Marine Science and Engineering, 2021 The accurate calculation of the sound field is one of the most concerning issues in hydroacoustics. The one-dimensional spectral method has been used to correctly solve simplified underwater acoustic propagation models, but it is difficult to solve ...
Xian Ma +5 more
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An efficient quantum partial differential equation solver with chebyshev points
Scientific Reports, 2023 Differential equations are the foundation of mathematical models representing the universe’s physics. Hence, it is significant to solve partial and ordinary differential equations, such as Navier–Stokes, heat transfer, convection–diffusion, and wave ...
Furkan Oz, O. San, Kursat Kara
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Fractal and Fractional, 2023 In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE).
W. Abd-Elhameed +3 more
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Computational and Applied Mathematics, 2022 This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE).
A. G. Atta, Youssri Hassan Youssri
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JTAM (Jurnal Teori dan Aplikasi Matematika), 2021 In this article, we discuss the Chebyshev Polynomial and its characteristics. The second order difference equation and the process obtaining the explicit solution of the Chebyshev polynomial have been given for each real number.
Ikhsan Maulidi +3 more
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Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation
Fractal and Fractional, 2022 In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials (5CPs), are used.
A. G. Atta +3 more
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