A Fully Discrete Galerkin Method for Integral and Pseudo differential Equations on Closed Curves

Abstract

We propose a cheep fully discrete version of the trigonometric Galerkin method of optimal accuracy order for integral and pseudodifferential equations on closed curves. A practical implementation of the method leads to a band system of linear algebraic equations. The error analysis is based on a thorough study of related integral operators in Sobolev spaces of periodic functions.