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Analytical and numerical aspects of certain nonlinear evolution equations. III. Numerical, Korteweg-de Vries equation. (English) Zbl 0541.65083

Summary: [For part II see the article reviewed above.]
Various numerical methods are used in order to approximate the Korteweg- de Vries equation, namely: (i) Zabusky-Kruskal scheme, (ii) hopscotch method, (iii) a scheme due to Goda, (iv) a proposed local scheme, (v) a proposed global scheme, (vi) a scheme suggested by Kruskal, (vii) split step Fourier method by Tappert, (viii) an improved split step Fourier method, and (ix) pseudospectral method by Fornberg and Whitham. Comparisons between our proposed scheme, which is developed using notions of the inverse scattering transform, and the other utilized schemes are obtained.

MSC:

65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application

Citations:

Zbl 0541.65082
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Full Text: DOI

References:

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