Une m�thode num�rique pour le calcul des points de retournement. Application � un probl�me aux limites non-lin�aire

Abstract

A finite element method (P~) with numerical integration for approximating the boundary value problem -Au=2e" is considered. It is shown that the discrete problem has a solution branch (with turning point) which converges uniformely to a solution branch of the continuous problem. Error estimates are given; for example it is found that I20-2~ =0(hZ-~), e>0, where 2 o and 2 o are critical values of the parameter 2 for continuous and discrete problems.

On a Class of Nonlinear Equation Solvers Based on the Residual Norm Reduction over a Sequence of Affine Subspaces

“…For all problems, the order of the system was equal to n 31 x 31 961, and the nearly critical value c 6.8 was chosen (it is known that c 6.808 is close to the limit point value; cf. [31 ], [26]). The corresponding iteration data are presented in Tables 1-4.…”

A projection method for computing turning points of nonlinear equations

“…[6], [18], [22], [23]) show that, if suitable discretizations are employed, then simple turning points are inherited by the approximating problem. The results of all our numerical experiments stress that the properties of the method on the underlying infinite dimensional problems are retained after discretizations and that the speed of convergence of the procedure applied to the corresponding discretized problems is unaffected by the increasing number of mesh points.…”

The approximation of generalized turning points\newline by Krylov subspace methods

“…. A detailed discussion on this problem can be found in [15]. To this example we applied Scheme 2, with B and X 0 null, for the three levels corresponding to the values n = 8, 16, 32.…”