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Progress in Industrial Mathematics at ECMI 2008

Volume 15 of the series Mathematics in Industry pp 69-87

Date:

Chebfun: A New Kind of Numerical Computing

  • R. B. PlatteAffiliated withSchool of Mathematical and Statistical Sciences, Arizona State University Email author 
  • , L. N. TrefethenAffiliated withOxford University Mathematical Institute

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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.