Modified deflation algorithm for the solution of singular problems. II. Nonlinear multipoint boundary value problems

Various kinds of iterative methods have been proposed for the solution of nonlinear multipoint boundary-value problems MPBVP's. However, it is necessary for these methods that the adjusting matrix, which corresponds to the Jacobian of nonlinear equations, is nonsingular at the solution. In this paper an algorithm for the singular solution of nonlinear MPBVP's, which is an extension of the modified deflation algorithm for the singular root of nonlinear algebraic equations developed by the author is presented. According to the present method, the singular solution can ultimately be reduced to the usual simple solution and both convergency and accuracy can greatly be improved. The effectiveness of the present method is shown by solving two illustrative examples.