Chebyshev polynomials in the numerical solution of differential equations

Authors:
A. G. Morris and T. S. Horner

Journal:
Math. Comp. **31** (1977), 881-891

MSC:
Primary 65L10

MathSciNet review:
0443359

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Amongst satisfactory techniques for the numerical solution of differential equations, the use of Chebyshev series is often avoided because of the tedious nature of the calculations. A systematic application of the Chebyshev method is given for certain fourth order boundary value problems in which the derivatives have polynomial coefficients. Numerical results for various problems using the Chebyshev method are superior to those obtained by alternative methods.

**[1]**C. W. Clenshaw,*The numerical solution of linear differential equations in Chebyshev series*, Proc. Cambridge Philos. Soc.**53**(1957), 134–149. MR**0082196****[2]**L. Fox and I. B. Parker,*Chebyshev polynomials in numerical analysis*, Oxford University Press, London-New York-Toronto, Ont., 1968. MR**0228149****[3]**J. G. F. Francis,*The 𝑄𝑅 transformation: a unitary analogue to the 𝐿𝑅 transformation. I*, Comput. J.**4**(1961/1962), 265–271. MR**0130111****[4]**Linda Kaufman,*The 𝐿𝑍-algorithm to solve the generalized eigenvalue problem*, SIAM J. Numer. Anal.**11**(1974), 997–1024. MR**0373253****[5]**C. B. Moler and G. W. Stewart,*An algorithm for generalized matrix eigenvalue problems*, SIAM J. Numer. Anal.**10**(1973), 241–256. Collection of articles dedicated to the memory of George E. Forsythe. MR**0345399****[6]**M. R. Osborne,*Numerical methods for hydrodynamic stability problems*, SIAM J. Appl. Math.**15**(1967), 539–557. MR**0243745****[7]***Mathematical methods for digital computers. Vol. II*, Edited by Anthony Ralston and Herbert S. Wilf, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR**0211638**

Retrieve articles in *Mathematics of Computation*
with MSC:
65L10

Retrieve articles in all journals with MSC: 65L10

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1977-0443359-7

Article copyright:
© Copyright 1977
American Mathematical Society