Fast Galerkin method and its application to determine periodic solutions of nonlinear oscillators
The Galerkin method is an approximate method which finds wide application in solving differential and integral equations. But a large amount of computation is needed in order to get a high order approximation by using the method. Applying the FFT technique to form a so-called fast Galerkin method we can reduce the computation work greatly, when taking trigonometric functions as characteristic functions. Taking the periodic solution of nonlinear oscillators as an example, we illustrate the procedure and the efficiency of the method. Moreover, with some modifications we extend the applicability of the method, so that not only periodic solutions with known periods, but also those with unknown periods, as well as subharmonics, combination tones, etc., can be treated with the method. Some techniques are described which can be used to simplify the computation.
trigonometric functions as characteristic functions
periodic solution of nonlinear oscillators
scientific article; zbMATH DE number 3980604