Chebyshev polynomials in the numerical solution of differential equations
HTML articles powered by AMS MathViewer
- by A. G. Morris and T. S. Horner PDF
- Math. Comp. 31 (1977), 881-891 Request permission
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.References
- C. W. Clenshaw, The numerical solution of linear differential equations in Chebyshev series, Proc. Cambridge Philos. Soc. 53 (1957), 134β149. MR 82196, DOI 10.1017/s0305004100032072
- L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London-New York-Toronto, Ont., 1968. MR 0228149
- J. G. F. Francis, The $QR$ transformation: a unitary analogue to the $LR$ transformation. I, Comput. J. 4 (1961/62), 265β271. MR 130111, DOI 10.1093/comjnl/4.3.265
- Linda Kaufman, The $LZ$-algorithm to solve the generalized eigenvalue problem, SIAM J. Numer. Anal. 11 (1974), 997β1024. MR 373253, DOI 10.1137/0711078
- C. B. Moler and G. W. Stewart, An algorithm for generalized matrix eigenvalue problems, SIAM J. Numer. Anal. 10 (1973), 241β256. MR 345399, DOI 10.1137/0710024
- M. R. Osborne, Numerical methods for hydrodynamic stability problems, SIAM J. Appl. Math. 15 (1967), 539β557. MR 243745, DOI 10.1137/0115048
- Anthony Ralston and Herbert S. Wilf (eds.), Mathematical methods for digital computers. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1967. MR 0211638
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Math. Comp. 31 (1977), 881-891
- MSC: Primary 65L10
- DOI: https://doi.org/10.1090/S0025-5718-1977-0443359-7
- MathSciNet review: 0443359