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Solving partial differential equations using sinc methods
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. ^
Bockelman, Brian Paul, "Solving partial differential equations using sinc methods" (2008). ETD collection for University of Nebraska - Lincoln. AAI3315327.