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Approximate solution of axially symmetric problems

1964; Association for Computing Machinery; Volume: 7; Issue: 6 Linguagem: Inglês

10.1145/512274.512292

1557-7317

Donald Greenspan,

Differential Equations and Numerical Methods

A variety of physical problems in such diverse fields as electrostatic field theory, heat and ideal fluid flow, and stress concentration theory reduce, under the assumption of axial symmetry, to the study of the elliptic partial differential equation ∂ 2 u/∂x 2 + ∂ 2 u/∂y 2 + k/y(∂u/∂y) = 0. Dirichlet-type problems associated with this equation are studied on regions whose boundaries include a nondegenerate portion of the x-axis and exceedingly accurate numerical methods are given for approximating solutions.