The Sinc-Galerkin Schwarz Alternating Method for Poisson’s Equation
Sinc-Galerkin and sinc-collocation methods provide a powerful and diverse set of tools for the numerical solution of differential equations. Sinc methods are particularly appealing because they can be used to solve problems with boundary singularities, while maintaining their characteristic exponential convergence rate. Since the introduction of the Sinc-Galerkin method in , sine methods have been used on a variety of differential equations, including the two-point boundary-value problem, Poisson’s equation, the wave equation, the heat equation, the advection-diffusion equation, and Burgers’ equation. In addition, sine methods have been successfully used in conjunction with more complex procedures such as domain decomposition (see , , , and ). A thorough convergence analysis for sine domain decomposition methods for ordinary differential equations is in  and .
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