Numerical computations for singular semilinear elliptic boundary value problems
The paper studies a class of Dirichlet problems with homogeneous boundary conditions for singular semilinear elliptic equations in a bounded smooth domain in R-n. A numerical method is devised to construct an approximate Green's function by using radial basis functions and the method of fundamental solutions. An estimate of the error involved is also given. A weak solution of the above given problem is a solution of its corresponding nonlinear integral equation. A computational method is given to find the minimal weak solution U, and the critical index lambda* (such that a weak solution U exists for lambda   lambda*). (C) 2002 Elsevier Science Ltd. All rights reserved.
dirichlet problem green's function radial basis functions method of fundamental solutions critical index thin plate spline parallel computations