On the approximation of nonlinear singular self-adjoint second order boundary value problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:224

Article

El-Gebeily, M. A.²  Furati, K. M.²  O'Regan, Donal³  Agarwal, Ravi¹ 

[1] Florida Inst Technol, Dept Math Sci, Melbourne, FL 32901 USA

[2] King Fahd Univ Petr & Minerals, Dept Math Sci, Dhahran 31261, Saudi Arabia

[3] Natl Univ Ireland, Dept Math, Galway, Ireland

关键词: Singular differential equations;    Self-adjoint operators;    Deficiency index;    Avoiding singularity;   

DOI  :  10.1016/j.cam.2008.05.038

来源: Elsevier

【 摘 要 】

We investigate the approximation of the solutions of a class of nonlinear second order singular boundary value problems with a self-adjoint linear part. Our strategy involves two ingredients. First. we take advantage of certain boundary condition functions to obtain well behaved functions of the solutions. Second, we integrate the problem over an interval that avoids the singularity. We are able to prove a uniform convergence result for the approximate solutions. We describe how the approximation is constructed for the various values of the deficiency index associated with the differential equation. The solution of the nonlinear problem is obtained by a globally convergent iterative method. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free