Novel Expressions for the Derivatives of Sixth Kind Chebyshev Polynomials: Spectral Solution of the Non-Linear One-Dimensional Burgers’ Equation [PDF]
Fractal and Fractional, 2021 This paper is concerned with establishing novel expressions that express the derivative of any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in terms of Chebyshev polynomials themselves.
Waleed Mohamed Abd-Elhameed
doaj +3 more sources
Solution for the System of Lane–Emden Type Equations Using Chebyshev Polynomials [PDF]
Mathematics, 2018 In this paper, we use the collocation method together with Chebyshev polynomials to solve system of Lane–Emden type (SLE) equations. We first transform the given SLE equation to a matrix equation by means of a truncated Chebyshev series with ...
Yalçın ÖZTÜRK
doaj +2 more sources
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
doaj +2 more sources
The Chebyshev Difference Equation
Mathematics, 2020 We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind.
Tom Cuchta +2 more
doaj +2 more sources
A Chebyshev-Based High-Order-Accurate Integral Equation Solver for Maxwell’s Equations [PDF]
IEEE Transactions on Antennas and Propagation, 2021 This article introduces a new method for discretizing and solving integral equation formulations of Maxwell’s equations, which achieves spectral accuracy for smooth surfaces.
Jin Hu +2 more
openalex +3 more sources
The Collocation Method Based on the New Chebyshev Cardinal Functions for Solving Fractional Delay Differential Equations [PDF]
MathematicsThe Chebyshev cardinal functions based on the Lobatto grid are introduced and used for the first time to solve the fractional delay differential equations.
Haifa Bin Jebreen, Ioannis Dassios
doaj +2 more sources
Discrete ordinates (SN) method for the first solution of the transport equation using Chebyshev polynomials [PDF]
EPJ Web of Conferences, 2016 First estimates for the numerical solution of the one-dimensional neutron transport equation for one-speed neutrons in a finite homogeneous slab is studied. The neutrons are assumed to be scattered isotropically through the medium.
Öztürk Hakan
doaj +2 more sources
Numerical solution of the Bagley–Torvik equation using shifted Chebyshev operational matrix
Advances in Difference Equations, 2020 In this study, an efficient numerical scheme based on shifted Chebyshev polynomials is established to obtain numerical solutions of the Bagley–Torvik equation. We first derive the shifted Chebyshev operational matrix of fractional derivative.
Tianfu Ji, Jianhua Hou, Changqing Yang
doaj +2 more sources
Shifted Chebyshev operational matrices to solve the fractional time-delay diffusion equation
Partial Differential Equations in Applied Mathematics, 2023 In this paper, Chebyshev operational matrices collocation technique is proposed for solution of variable order derivative within the fractional time-delay diffusion equation.
Adnan K. Farhood, Osama H. Mohammed
doaj +2 more sources
Solution of inverse heat conduction equation with the use of Chebyshev polynomials [PDF]
, 2016 A direct problem and an inverse problem for the Laplace’s equation was solved in this paper. Solution to the direct problem in a rectangle was sought in a form of finite linear combinations of Chebyshev polynomials.
Magda Joachimiak +2 more
openalex +2 more sources