The convergence of finite difference methods are examined in order to approximate the maximal solution of problems of the form u double prime lambda fx,u O, with boundary conditions either uO ub O or uO ub O, b 1. As this problem has in general more than one solution, two algorithms are developed to approximate solutions characterized by the number of their zeros in 0,1. The last section includes numerical results and some additional comments on the implementation of the algorithms on a digital computer.
Also available as Pub. 70-01 of the Universidad Central de Venezuela, Caracas. Departamento de Computacion.