TITLE:
The Lanczos-Chebyshev Pseudospectral Method for Solution of Differential Equations
AUTHORS:
Peter Y. P. Chen
KEYWORDS:
Solution of Differential Equations, Chebyshev Economized Power Series, Collocation Point Selection, Lanczos-Chebyshev Pseudospectral Method
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.9,
May
27,
2016
ABSTRACT: In this paper, we propose to replace the
Chebyshev series used in pseudospectral methods with the equivalent Chebyshev
economized power series that can be evaluated more rapidly. We keep the rest of
the implementation the same as the spectral method so that there is no new
mathematical principle involved. We show by numerical examples that the new
approach works well and there is indeed no significant loss of solution
accuracy. The advantages of using power series also include simplicity in its
formulation and implementation such that it could be used for complex systems.
We investigate the important issue of collocation point selection. Our
numerical results indicate that there is a clear accuracy advantage of using
collocation points corresponding to roots of the Chebyshev polynomial.