We present an enhancement of the generic fixpoint algorithm TD which can deal with widening and narrowing even for non-monotonic systems of equations. In constrast to corresponding enhancements proposed for other standard fixpoint algorithms, no extra priorities on variables are required. Still, a mechanism can be devised so that occurrences of the widening/narrowing operator are inserted as we...

We present a new algorithm for combining an anisotropic goal-oriented error estimate with the mesh adaptation fixed point method for unsteady problems. The minimization of the error on a functional provides both the density and the anisotropy (stretching) of the optimal mesh. They are expressed in terms of state and adjoint. This method is used for specifying the mesh for a time sub-interval. A...

In this paper we shall study a neutral differential equation with deviated argument in an arbitrary Banach space X. With the help of the analytic semigroups theory and fixed point method we establish the existence and uniqueness of solutions of the given problem. Finally, we give examples to illustrate the applications of the abstract results.

Using the fixed point method, we establish a generalized Ulam Hyers stability result for the monomial functional equation in the setting of complete random p-normed spaces. As a particular case, we obtain a new stability theorem for monomial functional equations in β-normed spaces.

In this paper, we prove a strong convergence result using a recently introduced iterative process with contractive-like operators. This improves andgeneralizes corresponding results in the literature in two ways: iterativeprocess is faster, operators are more general. At the end, we indicatethat the results can also be proved with the iterative process witherror terms. Keywords—Contractive-like...

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.

We consider thermal fluid structure interaction to model industrial gas quenching in steel forging, where hot steel is cooled using cold high pressured gas. This allows to define properties of the finished steel part, as for example yield strength, locally at low cost and without environmental problems. For the numerical simulation, a partitioned approach via a Dirichlet-Neumann coupling and a ...

The single-step one-shot method has proven to be very efficient for PDEconstrained optimization where the partial differential equation (PDE) is solved by an iterative fixed point solver. In this approach, the simulation and optimization tasks are performed simultaneously in a single iteration. If the PDE is unsteady, finding an appropriate fixed point iteration is nontrivial. In this paper, we...

Accurate modeling of availability is a practical problem in today’s complex high-availability systems. But as the system gets more complex, the state-space required for accurate modeling tends to grow very fast. In order to mitigate the largeness in model generation / solution, the system model could be divided into subsystem models, and solution for sub-models can be combined to yield overall ...

This study presents a new one-parameter family of the well-known fixed point iteration method for solving nonlinear equations numerically. The proposed is derived by implementing approximation through straight line. presence an arbitrary parameter in improves convergence characteristic simple as it has wider domain convergence. Furthermore, we propose many two-step predictor–corrector iterative...