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Taha, Thiab R.; Ablowitz, Mark J.

Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation. (English) Zbl 0541.65082

J. Comput. Phys. 55, 203-230 (1984).
Summary: [For part I see the article reviewed above.]
Various numerical methods are employed in order to approximate the nonlinear Schrödinger equation, namely: (i) The classical explicit method, (ii) hopscotch method, (iii) implicit-explicit method, (iv) Crank-Nicolson implicit scheme, (v) the Ablowitz-Ladik scheme, (vi) the split step Fourier method, and (vii) pseudospectral (Fourier) method. Comparisons between the Ablowitz-Ladik scheme, which was developed using notions of the inverse scattering transform, and the other utilized schemes are obtained.

Cited in 4 Reviews
Cited in 177 Documents

MSC:

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

Keywords:

pseudospectral method; nonlinear Schrödinger equation; explicit method; hopscotch method; implicit-explicit method; Crank-Nicolson implicit scheme; Ablowitz-Ladik scheme; split step Fourier method; Comparisons; inverse scattering

Citations:

Zbl 0541.65081
Cite Review PDF
Full Text: DOI

References:

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