On existence, uniqueness and convergence of approximate solution of boundary value problems related to the nonlinear operator Au :=-(k((u ')(2))u ')'+g(u)


Hasanov A.

APPLIED MATHEMATICS AND COMPUTATION, cilt.153, ss.659-672, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 153 Konu: 3
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1016/s0096-3003(03)00662-3
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Sayfa Sayısı: ss.659-672

Özet

We study the problems of solvability and linearization for the nonlinear boundary value problems with nonlinear operator Au := -(k ((u')(2)) u')' + g (u). Solvability in H-1[a,b] of the problems is obtained by using monotone potential operator theory and Browder-Minty theorem. Sufficient conditions for the solvability are obtained in explicit form. For the linearization of the considered nonlinear problems monotone iterative scheme is developed. The scheme permits use of the variational finite-difference scheme for the numerical solution the considered nonlinear problems. Sufficient conditions for the convergence of the iteration method are presented. Computational experiments illustrate high accuracy of the presented method. (C) 2003 Elsevier Inc. All rights reserved.