Results 171 to 180 of about 3,909 (206)

The Spectrum of the Chebyshev Collocation Operator for the Heat Equation

SIAM Journal on Numerical Analysis, 1983
Necessary and sufficient conditions on the coefficients for the time- stability of the equation: \((*)\quad u_ t=u_{xx}, | x|0\) are given. The authors review and modify some conditions which assure that a polynomial has negative, real and distinct roots. The collocation Chebyshev method for the equation (*) is studied.
David Gottlieb, Liviu Lustman
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On the Chebyshev solution of inconsistent linear equations

BIT, 1968
A new formulation of the ascent algorithm for the Chebyshev solution of linear systems is given. This leads to two algorithms, which are similar to the ordinary simplex and the product form of inverse algorithms for the solution of linear programming problems.
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Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations

SIAM Journal on Scientific Computing, 2010
This paper is concerned with the spectral Chebyshev collocation solution of the Dirichlet problems for the Poisson and biharmonic equations in a square. The collocation schemes are solved at a cost of $2N^3+O(N^2\log N)$ operations using an appropriate set of basis functions, a matrix diagonalization algorithm, and fast Fourier transforms.
Bialecki, B., Karageorghis, Andreas, Bialecki, B., Karageorghis, Andreas   +3 more
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Chebyshev series solutions of Fredholm integral equations

International Journal of Mathematical Education in Science and Technology, 1996
A matrix method for approximately solving certain linear and non‐linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Chebyshev series approximation. The method is based on first taking the truncated Chebyshev series expansions of the functions in equation and then substituting their matrix forms into ...
DOĞAN, SETENAY, SEZER, MEHMET
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Sturmian eigenvalue equations with a Chebyshev polynomial basis

Journal of Computational Physics, 1985
From authors' summary: A Chebyshev polynomial basis is proposed for the solution of Sturmian eigenvalue equations of the form \(Av=f\) which are encountered in quantum scattering theory. A is a non-self-adjoint second order differential operator and the solution is regular at the origin and has an outgoing wave condition asymptotically.
George Rawitscher, G. Delic
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Chebyshev solution of overdetermined systems of linear equations

BIT, 1975
A simplex algorithm for the Chebyshev solution of overdetermined systems of linear equations is described. In this algorithm, an initial basic feasible solution is available with no artificial variables needed. Also minimum storage is required and no conditions are imposed on the coefficient matrix. The algorithm is a simple and fast one.
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Chebyshev polynomial solutions of linear differential equations

International Journal of Mathematical Education in Science and Technology, 1996
A matrix method, which is called the Chebyshev‐matrix method, for the approximate solution of linear differential equations in terms of Chebyshev polynomials is presented. The method is based on first taking the truncated Chebyshev series of the functions in equation and then substituting their matrix forms into the given equation. Thereby the equation
Sezer, Mehmet, KAYNAK, MEHMET
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Solvability of a system of equations for the Fourier–Chebyshev coefficients when solving ordinary differential equations by the Chebyshev series method

Moscow University Mathematics Bulletin, 2017
A solvability theorem for a system of equations with respect to approximate values of Fourier–Chebyshev coefficients is formulated. This theorem is a theoretical justification for numerical solution of ordinary differential equations using Chebyshev series.
S. F. Zaletkin, O. B. Arushanyan
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Chebyshev series solution of the Thomas-Fermi equation

Computer Physics Communications, 1992
The numerical solution of the Thomas-Fermi equation is considered. Chebyshev series for small and large values of x are derived. Values of the coefficients to 10D are given.
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An Accurate Solution of the Poisson Equation by the Chebyshev Collocation Method

Journal of Computational Physics, 1993
In a first step the Chebyshev collocation method for solving the one- dimensional Poisson equation with homogeneous boundary conditions is developed and it is shown that the unknown coefficients of a truncated expansion of the solution with respect to Chebyshev polynomials can be found as the solution of an upper triangular linear system of equations ...
C. Delcarte, H. Dang-Vu
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