The numerical solution of linear differential equations in Chebyshev series
- 1 January 1957
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 53 (1) , 134-149
- https://doi.org/10.1017/s0305004100032072
Abstract
This paper describes a method for computing the coefficients in the Chebyshev expansion of a solution of an ordinary linear differential equation. The method is valid when the solution required is bounded and possesses a finite number of maxima and minima in the finite range of integration. The essence of the method is that an expansion in Chebyshev polynomials is assumed for the highest derivative occurring in the equation; the coefficients are then determined by integrating this series, substituting in the original equation and equating coefficients.Comparison is made with the Fourier series method of Dennis and Foots, and with the polynomial approximation method of Lanczos. Examples are given of the application of the method to some first and second order equations, including one eigenvalue problem.Keywords
This publication has 6 references indexed in Scilit:
- The solution of linear differential equationsMathematical Proceedings of the Cambridge Philosophical Society, 1955
- A note on the summation of Chebyshev seriesMathematics of Computation, 1955
- Notes on Numerical Analysis--3: Solution of Differential Equations by Recurrence RelationsMathematical Tables and Other Aids to Computation, 1951
- Some new methods for the numerical integration of ordinary differential equationsMathematical Proceedings of the Cambridge Philosophical Society, 1949
- The solution by relaxation methods of ordinary differential equationsMathematical Proceedings of the Cambridge Philosophical Society, 1949
- Trigonometric Interpolation of Empirical and Analytical FunctionsJournal of Mathematics and Physics, 1938