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  "body": "\n## Summary\n\nA pseudo-spectral method is a [[spectral method|MYV657YRDW]] that imposes the equation at grid points, by collocation.\nIt does not use integrals against the basis functions.\nDerivatives are computed in coefficient space, for example with the [[fast Fourier transform|S966EZX3ZT]], while products and other nonlinear terms are computed pointwise on the grid.\nThis keeps the accuracy of spectral methods at a much lower cost for nonlinear problems.\nThe price is aliasing errors from the pointwise products, which are often removed by padding or truncation.\nSee the [[definition|T37Q055GDA]].\n\n## Explanations\n\n### L1 human\n\nStore a function by its values at evenly spaced points around a circle.\nTo differentiate, turn the values into wave amplitudes, multiply each amplitude by its frequency times $i$, and turn the result back into values.\nTo multiply two functions, just multiply their values point by point.\nSwitching back and forth between values and amplitudes is fast, which makes the method efficient.\n",
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