Iterative bounds for the stable solutions of convex non-linear boundary value problems

Author:

Mooney J. W.,Roach G. F.

Abstract

SynopsisWe consider a class of convex non-linear boundary value problems of the formwhere L is a linear, uniformly elliptic, self-adjoint differential expression, f is a given non-linear function, B is a boundary differential expression of either Dirichlet or Neumann type and D is a bounded open domain with boundary ∂D. Particular problems of this class arise in the process of thermal combustion [8].In this paper we show that stable solutions of this class can be bounded from below (above) by a monotonically increasing (decreasing) sequence of Newton (Picard) iterates. The possibility of using these schemes to construct unstable solutions is also considered.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Iterative methods for a singular boundary-value problem;Journal of Computational and Applied Mathematics;1999-11

2. NUMERICAL SOLUTION OF A SUBLINEAR SINGULAR BOUNDARY-VALUE PROBLEM;EPMESC VII;1999

3. Numerical schemes for degenerate boundary value problems;Journal of Physics A: Mathematical and General;1993-04-21

4. On the positive solutions of some nonlinear diffusion problems;ZAMP Zeitschrift f�r angewandte Mathematik und Physik;1985-07

5. Newton Iterates for Positive Solutions of a Class of Nonlinear Eigenvalue Problems;Numerical Methods for Bifurcation Problems;1984

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