Computational methods for a singular boundary-value problem

methods to the numerical solution of singular boundary value problems which describe the deformation of a membrane cap. The considered differential equation may be written in the form r(2)S(r) + 3rS(r) = lambda(2)/2 r(2gamma-2) + betanur(2)/S-r - r(2)/8S(r)(2) r is an element of (0,1] where S-r, r and nu denote a the radial stress, the membrane radius and the Poisson coefficient, respectively, gamma, lambda and beta are known positive constants. We shall look for a positive solution S, which satisfies the following boundary conditions S-r is bounded at 0 and S-r(1)+(1-nu)S-r(1)=beth or S-r(1)=S, (2) where beth and S are real numbers. By using well-known iterative methods, like the Picard and Newton's method, the nonlinear problem is reduced to a sequence of linear ones, which are then discretized by the finite differences method. The numerical results obtained by the finites difference method are compared with the ones presented in other papers and the efficiency of different numerical methods is discussed.