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Chebfun: A new kind of numerical computing. (English) Zbl 1220.65100

Fitt, Alistair D. (ed.) et al., Progress in industrial mathematics at ECMI 2008. Proceedings of the 15th European conference on mathematics for industry, London, UK, June 30 - July 4, 2008. Berlin: Springer (ISBN 978-3-642-12109-8/hbk; 978-3-642-12110-4/ebook). Mathematics in Industry 15, 69-87 (2010).
Summary: The functionalities of the chebfun and chebop systems are surveyed. The chebfun system is a collection of Matlab codes to manipulate functions in a manner that resembles symbolic computing. The operations, however, are performed numerically using polynomial representations. Chebops are built with the aid of chebfuns to represent linear operators and allow chebfun solutions of differential equations. In this article we present examples to illustrate the simplicity and effectiveness of the software. Among other problems, we consider edge detection in logistic map functions and the solution of linear and nonlinear differential equations.
For the entire collection see [Zbl 1197.00055].

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
68W30 Symbolic computation and algebraic computation
65Y15 Packaged methods for numerical algorithms
34B05 Linear boundary value problems for ordinary differential equations
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
65D15 Algorithms for approximation of functions
35K20 Initial-boundary value problems for second-order parabolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)

Software:

Chebfun; chebop; Matlab
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