32 citations · 60 across the 5 of their papers we have counts for
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A Spectral Method for Nonlinear Elliptic Equations
Kendall Atkinson, David Chien, Olaf Hansen
Let be an open, simply connected, and bounded region in , , and assume its boundary is smooth. Consider solving an elliptic partial differen…
Evaluating Polynomials Over the Unit Disk and the Unit Ball
Kendall Atkinson, Olaf Hansen, David Chien
We investigate the use of orthonormal polynomials over the unit disk B_2 in R^2 and the unit ball B_3 in R^3. An efficient evaluation of an orthonormal polynomial basis is given, a…
A Spectral Method for Parabolic Differential Equations
Kendall Atkinson, Olaf Hansen, David Chien
We present a spectral method for parabolic partial differential equations with zero Dirichlet boundary conditions. The region Ω for the problem is assumed to be simply-connected an…
A Spectral Method for Elliptic Equations: The Neumann Problem
Kendall Atkinson, David Chien, Olaf Hansen
Let be an open, simply connected, and bounded region in , , and assume its boundary is smooth. Consider solving an elliptic partial differen…
A spectral method for elliptic equations: the Dirichlet problem
Kendall Atkinson, David Chien, Olaf Hansen
An elliptic partial differential equation Lu=f with a zero Dirichlet boundary condition is converted to an equivalent elliptic equation on the unit ball. A spectral Galerkin method…