Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation. (English) Zbl 0541.65082
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.
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.
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 scatteringCitations:
Zbl 0541.65081References:
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