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Investigations of nonstandard, Mickens-type, finite difference schemes for singular boundary value problems in cylindrical or spherical coordinates. (English) Zbl 1079.76048
The author introduces new finite difference schemes to solve singular boundary value problems for differential equations in cylindrical or spherical coordinates. The results of the paper show that these schemes appear to tackle singular value problems more accurately and efficiently than standard finite difference schemes. Although the initial discovery of these particular Mickens-type finite differences was motivated by a problem in theoretical aerodynamics in cylindrical coordinates, the schemes explicated within this paper can really be used for any problem where the Laplacian operator in cylindrical or spherical coordinates needs to be discretized numerically.
MSC:
76M20Finite difference methods (fluid mechanics)
65N06Finite difference methods (BVP of PDE)