NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS WITH MULTIPLE SOLUTIONS.
Abstract
The convergence of finite difference methods are examined in order to approximate the maximal solution of problems of the form: u double prime + lambda f(x,u) = O, with boundary conditions either u(O) = u(b) = O or u(O) = u'(b) = 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0701684
Entities
People
- Seymour V. Parter
- Victor Pereyra
Organizations
- University of Wisconsin–Madison