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ELLIPTIC EQUATIONS IN UNBOUNDED DOMAINS

Mathematics of the USSR-Sbornik, 1971
A linear differential operator in of elliptic type, with varying coefficients, is considered along with a boundary value problem for such an operator in the exterior of a bounded region. Certain conditions on the symbol of the operator are assumed, the formulation of which involves lower-order terms.
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A Spectral Method for Unbounded Domains

Journal of Computational Physics, 1997
The spectral method for an unbounded domain is developed and presented. For the expansion in the radial direction of polar coordinates \((r,\varphi)\) or \((r, \varphi, z)\) rational basis functions which are algebraically mapped Legendre functions are used.
Matsushima, T., Marcus, P. S.
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