Search results for "Nonlinear system"

Improving the stability bound for the PPH nonlinear subdivision scheme for data coming from strictly convex functions

2021

Abstract Subdivision schemes are widely used in the generation of curves and surfaces, and therefore they are applied in a variety of interesting applications from geological reconstructions of unaccessible regions to cartoon film productions or car and ship manufacturing. In most cases dealing with a convexity preserving subdivision scheme is needed to accurately reproduce the required surfaces. Stability respect to the initial input data is also crucial in applications. The so called PPH nonlinear subdivision scheme is proven to be both convexity preserving and stable. The tighter the stability bound the better controlled is the final output error. In this article a more accurate stabilit…

A nonlinear Chaikin-based binary subdivision scheme

2019

Abstract In this work we introduce and analyze a new nonlinear subdivision scheme based on a nonlinear blending between Chaikin’s subdivision rules and the linear 3-cell subdivision scheme. Our scheme seeks to improve the lack of convergence in the uniform metric of the nonlinear scheme proposed in Amat et al. (2012), where the authors define a cell-average version of the PPH subdivision scheme (Amat et al., 2006). The properties of the new scheme are analyzed and its performance is illustrated through numerical examples.

Mathematical Modeling and Optimization of a Vehicle Crash Test based on a Single-Mass

2014

In this paper mathematical modelling of a vehicle crash test based on a single mass is studied. The models under consideration consist of a single mass, a spring and/or a damper. They are constructed according to the measured vehicle speed before the collision and measured vehicle accelerations in three directions at the centre of gravity. A new model of nonlinear spring-mass-damper is also proposed to describe the crash. Simulation results are provided to show the effectiveness and applicability of the proposed methods.

Non-fragile fuzzy control design for nonlinear time-delay systems

2013

In this paper, a non-fragile fuzzy control design is proposed for a class of nonlinear systems with mixed discrete and distributed time delays. The Takagi and Sugeno (T-S) fuzzy set approach is applied to the modelling of the nonlinear dynamics, and a T-S fuzzy model is constructed, which can represent the nonlinear system. Then, based on the fuzzy linear model, a fuzzy linear controller is developed to stabilize the nonlinear system. The control law is obtained to ensure stochastically exponentially stability in the mean square. The sufficient conditions for the existence of such a control are proposed in terms of certain linear matrix inequalities.

Random attractors for stochastic lattice systems with non-Lipschitz nonlinearity

2011

In this article, we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an additive noise. We do not assume any Lipschitz condition on the nonlinear term, just a continuity assumption together with growth and dissipative conditions so that uniqueness of the Cauchy problem fails to be true. Using the theory of multi-valued random dynamical systems, we prove the existence of a random compact global attractor.

A parallel splitting up method and its application to Navier-Stokes equations

1991

A parallel splitting-up method (or the so called alternating-direction method) is proposed in this paper. The method not only reduces the original linear and nonlinear problems into a series of one dimensional linear problems, but also enables us to compute all these one dimensional linear problems by parallel processors. Applications of the method to linear parabolic problem, steady state and nonsteady state Navier-Stokes problems are given. peerReviewed

Stabilization of solutions of the filtration equation with absorption and non-linear flux

1995

This paper is primarily concerned with the large time behaviour of solutions of the initial boundary value problem $$\begin{gathered} u_t = \Delta \phi (u) - \varphi (x,u)in\Omega \times (0,\infty ) \hfill \\ - \frac{{\partial \phi (u)}}{{\partial \eta }} \in \beta (u)on\partial \Omega \times (0,\infty ) \hfill \\ u(x,0) = u_0 (x)in\Omega . \hfill \\ \end{gathered} $$ Problems of this sort arise in a number of areas of science; for instance, in models for gas or fluid flows in porous media and for the spread of certain biological populations.

Types of solutions and multiplicity results for two-point nonlinear boundary value problems

2005

Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. If the respective nonlinear equation can be reduced to a quasi-linear one with a non-resonant linear part and both equations are equivalent in some domain D , and if solutions of the quasi-linear problem lie in D , then the original problem has a solution. We then say that the original problem allows for quasilinearization. We show that a quasi-linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.

Sharp conditions for rapid nonlinear oscillations

2000

Global existence and uniqueness result for the diffusive Peterlin viscoelastic model

2015

Abstract The aim of this paper is to present the existence and uniqueness result for the diffusive Peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids. The polymers are treated as two beads connected by a nonlinear spring. The Peterlin approximation of the spring force is used to derive the equation for the conformation tensor. The latter is the time evolution equation with spatial diffusion of the conformation tensor. Using the energy estimates we prove global in time existence of a weak solution in two space dimensions. We are also able to show the regularity and consequently the uniqueness of the weak solution.