scholarly journals Synchronization in coupled second order in time infinite-dimensional models

2016 ◽  
Vol 13 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Igor Chueshov
Keyword(s):  
Second Order ◽  
Infinite Dimensional ◽  
Second Order In Time ◽  
Dimensional Models

scholarly journals An adaptive control scheme for hyperbolic partial differential equation system (drilling system) with unknown coefficient

2017 ◽  
Vol 27 (1) ◽  
pp. 63-76
Author(s):  
Hamed Shirinabadi Farahani ◽  
Heidar Ali Talebi ◽  
Mohammad Baghermenhaj
Keyword(s):  
Equation System ◽  
Second Order ◽  
Unknown Coefficient ◽  
Hyperbolic Pde ◽  
Control Approach ◽  
Infinite Dimensional ◽  
Control Scheme ◽  
Full State ◽  
Drilling System ◽  
Second Order In Time

Abstract The adaptive boundary stabilization is investigated for a class of systems described by second-order hyperbolic PDEs with unknown coefficient. The proposed control scheme only utilizes measurement on top boundary and assume anti-damping dynamics on the opposite boundary which is the main feature of our work. To cope with the lack of full state measurements, we introduce Riemann variables which allow us reformulate the second-order in time hyperbolic PDE as a system with linear input-delay dynamics. Then, the infinite-dimensional time-delay tools are employed to design the controller. Simulation results which applied on mathematical model of drilling system are given to demonstrate the effectiveness of the proposed control approach.

scholarly journals An Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Lei Ren ◽  
Lei Liu
Keyword(s):  
Finite Difference ◽  
Fourth Order ◽  
Difference Method ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Formula ◽  
Discrete Energy ◽  
Compact Finite Difference ◽  
Second Order In Time

In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2-α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the L2-1σ approximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.

scholarly journals Linear second-order IMEX-type integrator for the (eddy current) Landau–Lifshitz–Gilbert equation

2019 ◽  
Vol 40 (4) ◽  
pp. 2802-2838 ◽  
Author(s):  
Giovanni Di Fratta ◽  
Carl-Martin Pfeiler ◽  
Dirk Praetorius ◽  
Michele Ruggeri ◽  
Bernhard Stiftner
Keyword(s):  
Eddy Current ◽  
Maxwell Equations ◽  
Coupled System ◽  
Second Order ◽  
Stray Field ◽  
Time Step ◽  
Finite Element Scheme ◽  
Second Order In Time ◽  
Current Approximation ◽  
Numer Math

Abstract Combining ideas from Alouges et al. (2014, A convergent and precise finite element scheme for Landau–Lifschitz–Gilbert equation. Numer. Math., 128, 407–430) and Praetorius et al. (2018, Convergence of an implicit-explicit midpoint scheme for computational micromagnetics. Comput. Math. Appl., 75, 1719–1738) we propose a numerical algorithm for the integration of the nonlinear and time-dependent Landau–Lifshitz–Gilbert (LLG) equation, which is unconditionally convergent, formally (almost) second-order in time, and requires the solution of only one linear system per time step. Only the exchange contribution is integrated implicitly in time, while the lower-order contributions like the computationally expensive stray field are treated explicitly in time. Then we extend the scheme to the coupled system of the LLG equation with the eddy current approximation of Maxwell equations. Unlike existing schemes for this system, the new integrator is unconditionally convergent, (almost) second-order in time, and requires the solution of only two linear systems per time step.

scholarly journals Second order tangent bundles of infinite dimensional manifolds

2004 ◽  
Vol 52 (2) ◽  
pp. 127-136 ◽  
Author(s):  
C.T.J. Dodson ◽  
G.N. Galanis
Keyword(s):  
Second Order ◽  
Infinite Dimensional ◽  
Tangent Bundles ◽  
Order Tangent
Sign in / Sign up

Export Citation Format

Share Document