The fast solution of periodic pseudodifferential equations

Abstract

We construct a fast algorithm for the solution of periodic pseudodifferential equations, which, additionally, has a higher order convergence rate in Sobolev spaces with negative order than the collocation method. The first step of our algorithm consists in using a parametrix for the pseudodifferential operator in order to get an approximate solution on a fine grid. In a second step this solution is corrected by the solution of a Galerkin scheme on a coarse grid. Both trigonometric and spline approximation methods are considered.

Keywords:

• Periodic pseudodifferential equation
• approximation method
• fast Fourier transormation.

^*This work was supported by the Priority Research Program “Boundary Element Methods” of the German Research Foundation(Deutsche Forschungsgemeinschaft)

^*This work was supported by the Priority Research Program “Boundary Element Methods” of the German Research Foundation(Deutsche Forschungsgemeinschaft)

Notes

^*This work was supported by the Priority Research Program “Boundary Element Methods” of the German Research Foundation(Deutsche Forschungsgemeinschaft)