A simple and efficient algorithm is proposed for the numerical solution of the non-linear Schrödinger equation. Operator splitting is used, as with the split-step-Fourier method, in order to treat the linear part and the non-linear part of the equation separately. However, in our method, the FFT solution of the linear part is replaced by a very accurate Gauss-Hermite orthogonal expansion. Gaussian quadrature nodes and weights are used in order to calculate the expansion coefficients. Our methods is found to be very accurate and faster than the split-step-Fourier method for the model problem of single soliton propagation.
|Number of pages||5|
|Journal||International Journal of Numerical Modelling: Electronic Networks, Devices and Fields|
|Early online date||16 Mar 2001|
|Publication status||Published - Jul 2001|