Journal Article10.1080/00207167508803102
A practical chebyshev collocation method for differential equations
7
TL;DR: The main feature of the method, which is based on the collocation principle, is that it solves the problem of differentiating a Chebyshev series directly by the use of a stable recurrence relation.
read more
Abstract: This paper describes a method for solving ordinary and partial differential equations in Chebyshev series. The main feature of the method, which is based on the collocation principle, (Lanczos [8]) is that it solves the problem of differentiating a Chebyshev series directly by the use of a stable recurrence relation. As a practical consequence the method is very simple and can easily be coded into a general-purpose program for solving some differential equations.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
TL;DR: In this paper, a formula for the ultraspherical coefficients of the moments of one single polynomial of a certain degree is given and corresponding formulae for the important special cases of Chebyshev polynomials of the first and second kinds and of Legendre polynomorphisms are deduced.
35
Legendre expansion method for the solution of the second-and fourth-order elliptic equations
TL;DR: The suggested method is applicable for a wide area of differential equations and is in satisfactory agreement with the exact solutions of the second-and fourth-order elliptic equation.
16
On the legendre coefficients of the moments of the general order derivative of an infinitely differentiable function
Eid H. Doha,S. I. El-Soubhy +1 more
TL;DR: Two numerical applications of how to use these formulae for solving ordinary differential equations with varying coefficients, by reducing them to recurrence relations of lowest order in the Legendre expansion coefficients are discussed.
9
Chebyshev polynomials in the solution of ordinary and partial differential equations
T. S. Horner
- 01 Jan 1977
TL;DR: Chebyshev polynomials are used to obtain accurate numerical solutions of ordinary and partial differential equations as mentioned in this paper, and generalisations of formulae for finding function and derivative values.
The use of Chebyshev series in computational physics
TL;DR: A survey of the current uses and techniques involving Chebyshev series in computational methods in physics introduces applications principally in differential and integral equations.
3