Solving partial differential equations using sinc methods

Brian Paul Bockelman, University of Nebraska - Lincoln

Abstract

Sinc methods, since their introduction, have shown great theoretical promise as highly accurate methods for a wide range of numerical tasks. They have proven to have exponential convergence for ordinary differential equations and partial differential equations. However, there are few large-scale numerical implementations of sinc methods due to the density and size of the resulting matrix equations. We have developed a package, SincLib, which provides significant computational improvements for sinc-based PDE solutions in n -dimensions. We apply these speedups to several problems on different types of computational hardware. We additionally discuss domain decomposition as a method for attacking problems which are not differentiable at points. Throughout the dissertation, we apply our work to problems arising from the Schrödinger equation and the Poisson equation.

Recommended Citation

Brian Paul Bockelman, "Solving partial differential equations using sinc methods" (January 1, 2008). ETD collection for University of Nebraska - Lincoln. Paper AAI3315327.
http://digitalcommons.unl.edu/dissertations/AAI3315327