Spectral methods

Spectral methods are mathematical techniques used to analyze complex systems by breaking them down into fundamental components called "spectra," often represented by functions like sine and cosine waves. They are widely used in fields such as physics, engineering, and data analysis to solve differential equations or identify underlying patterns. Think of it like tuning a musical instrument to separate different notes; spectral methods identify and manipulate the basic "notes" that make up more complicated signals or phenomena, allowing precise analysis and solution of problems involving waves, vibrations, or other continuous processes.