Nonlinear implicit iterative method for solving nonlinear ill-posed problems

Abstract

In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.

Influence of porosity on resistivity of polypropylene foams

“…Liu et al 7,8 developed a theoretical model for dc conductivity of foam material based on body-centered structures. This model takes into account the shape of the inclusions, as well as the volume fractions of the component phases.…”

“…In situ foam, developed by adding the foaming agent to PP, will be different from the foams analyzed by Liu et al 7,8 It is necessary to modify the Liu et al model to suit the electrical resistivity behavior of PP foams having different densities. The theoretical model related to conduction in porous materials discussed by Liu was modified to suit the conduction mechanism in PP foam.…”

“…The thin-walled cellular structure foam polymers have advantages of low density and provide enhanced thermal and electrical insulation properties as compared to higher density. Liu et al 7,8 reported a theoretical model for dc conductivity for foam composites. Fu et al proposed a statistical model {Log( ó ) −6.63 + 0.28 c 0.43} for conductivity of foam materials, which is related to the effect of the density on the integrity of the percolation network.…”

“…In this article, an effort has been made to prepare polypropylene (PP) foam, having different densities. Liu et al 7,8 model, is modified by replacing the preparation parameter by a new constant, which is obtained from estimated porosity.…”

Estimation of heat transfer coefficients and heat flux on the billet surface by an integrated approach

“…That is to say, the surface temperature measurements with small error can create large disturbance in the results. The classical Levenberg-Marquardt (LM) [15][16][17][18] algorithm is a valid method for solving this nonlinear inverse heat transfer problem. Recently, many research works [19][20][21] focus on improving this algorithm with non-exact line search.…”