Numerical Analysis Questions
Spectral methods for solving differential equations involve representing the solution of the differential equation as a sum of basis functions, typically chosen to be orthogonal or nearly orthogonal. These basis functions are often chosen to be trigonometric functions or polynomials. By expanding the solution in terms of these basis functions, the differential equation can be transformed into a system of algebraic equations, which can then be solved numerically. Spectral methods are known for their high accuracy and efficiency in solving differential equations, particularly for problems with smooth solutions.