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

摘要

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 H1[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.