Stable spectral collocation solutions to Cauchy problems for nonlinear dispersive wave equations

Abstract

In this paper we are concerned with accurate and stable spectral collocation solutions to initial-boundary value problems attached to some challenging nonlinear wave equations defined on unbounded domains. We argue that spectral collocation based on Hermite and sinc functions actually provide such solutions avoiding the empirical domain truncation or any shooting techniques.

Authors

Călin-Ioan Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Keywords

Hermite; sinc; collocation; nonlinear; wave equation; shock like solution.

References

See the expanding block below.

Cite this paper as

C.I. Gheorghiu, Stable spectral collocation solutions to Cauchy problems for nonlinear dispersive wave equations, Proceedings of the 4th Conference of Mathematical Society of Moldova (CMSM4), 2017, pp. 277-280. ISBN 978-9975-71-915-5

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About this paper

Journal

Proceedings of the 4th Conference of Mathematical Society of Moldova

Publisher Name

Academy of Sciences of Moldova

DOI
ISBN

ISBN 978-9975-71-915-5

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References

References

[1] J.P. Boyd. Spectral Methods Using Rational Basis Functions on an Infinite interval. J. Comput. Phys., 69 (1987), pp. 112–142.

[2] B. Fornberg, A. Driscoll. A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion, J. Comput. Phys., 155 (1999), pp. 456–467.

[3] C.I. Gheorghiu, Spectral Methods for Non Standard Eigenvalue Problems. Fluid and Structural Mechanics and Beyond. Springer, 2014.

[4] C.I. Gheorghiu. Stable spectral collocation solutions to a class of Benjamin Bona Mahony initial value problems, Appl. Math. Comput. vol. 273 (2016), pp. 1090–1099.

[5] C.I. Gheorghiu. High Order Collocation Solutions to Problems on Unbounded Domains. Manuscript in progress.

[6] L.N. Trefethen. Spectral Methods in Matlab, SIAM Philadelphia, 2000.

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