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Line 35: ==Numerical methods== Both ''spatial ___domain'' methods, and ''frequency (spectral) ___domain'' methods are available for the numerical solution of the discretized master equation. Upon discretization into a grid, (using various [[central difference\|centralized difference]], [[~~Crank Nicolson~~Crank–Nicolson method]], FFT-BPM etc.) and field values rearranged in a causal fashion, the field evolution is computed through iteration, along the propagation direction. The spatial ___domain method computes the field at the next step (in the propagation direction) by solving a linear equation, whereas the spectral ___domain methods use the powerful forward/inverse [[Fast Fourier transform\|DFT]] algorithms. Spectral ___domain methods have the advantage of stability even in the presence of nonlinearity (from refractive index or medium properties), while spatial ___domain methods can possibly become numerically unstable. ==Applications==

Beam propagation method: Difference between revisions