= Harmonic balance
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Harmonic balance substitutes a finite <Fourier series> into a differential equation and projects the residual onto the retained harmonics. It determines their amplitudes and phases. A nonlinear equation generally generates additional harmonics, so vanishing of the projected residual alone does not make the finite series an exact solution. In a <weakly nonlinear expansion>, nonresonant generated harmonics can be found at the next order by solving their linear equations.
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