Solution of singular elliptic PDEs on a union of rectangles using sinc methods. (English) Zbl 1112.65126
Summary: The numerical solution of problems with singularities presents special difficulties for most methods. Adjustments to standard methods are typically made for only a special type of singularity, usually known a priori. The family of sine numerical methods is naturally suited for general singular problems. Here, the methods are extended and applied to two-dimensional, elliptic first-order systems of mixed boundary value problems with singularities of the form \(x^\alpha\).
MSC:
65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
35J55 | Systems of elliptic equations, boundary value problems (MSC2000) |
65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |