Qualitative behavior and computation of multiple solutions of nonlinear boundary value problems
Grey Ballard - Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, NC 27109, United States (email)
Abstract: We consider nonlinear boundary value problems with multiple solutions. A method is proposed for the computation of such solutions which depends crucially on known a priori qualitative information about the behavior of the solutions. The method is a two-stage method where the second stage is a shooting method and initial values of the shooting parameters are found in a first stage which approximates the boundary value problem with a discrete approximation. Both nonsingular and singular problems are considered.
Keywords: Multiple solutions, qualitative behavior, shooting,
iterative methods, nonlinear boundary value problems.
Received: March 2005; Revised: June 2005; Published: March 2006.
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