ISSN:
1572-9125
Keywords:
65–60
;
65–62
;
34–36
;
Two-Point Boundary Value Problems
;
Nonlinear Eigenvalue Problems
;
Maximal Solutions
;
Positive Solutions
;
Heavy Rotating String
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In the first part of this paper we study the convergence of finite difference methods to approximate the maximal solution of problems of the form:u″+λf (x, u)=0, with boundary conditions eitheru(0)=u(b)=0 oru(0)=u′ (b)=0, 0〈b≦1. The functionf(x, u) satisfies several conditions that are explicitly given in § 1. This work extends earlier results of Parter (see references at the end). Since this problem has in general more than one solution we develop in the second part two algorithms to approximate solutions characterized by the number of their zeros in (0, 1). We include in the last Section numerical results and some additional comments on the implementation of the algorithms on a digital computer.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01935327
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