Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

The Fourier method for nonsmooth initial data


Authors: Andrew Majda, James McDonough and Stanley Osher
Journal: Math. Comp. 32 (1978), 1041-1081
MSC: Primary 65M10
DOI: https://doi.org/10.1090/S0025-5718-1978-0501995-4
MathSciNet review: 501995
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Application of the Fourier method to very general linear hyperbolic Cauchy problems having nonsmooth initial data is considered, both theoretically and computationally. In the absence of smoothing, the Fourier method will, in general, be globally inaccurate, and perhaps unstable. Two main results are proven: the first shows that appropriate smoothing techniques applied to the equation gives stability; and the second states that this smoothing combined with a certain smoothing of the initial data leads to infinite order accuracy away from the set of discontinuities of the exact solution modulo a very small easily characterized exceptional set. A particular implementation of the smoothing method is discussed; and the results of its application to several test problems are presented, and compared with solutions obtained without smoothing.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M10

Retrieve articles in all journals with MSC: 65M10


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1978-0501995-4
Keywords: Fourier method, hyperbolic equations, Cauchy problem, smoothing techniques, convergence rate, stability
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society