J. The sharp pointwise-in-time error estimate is given for the fully discrete ADI scheme, and the final error bound is alpha(1)-robust (i.e. the error bound does not blow up when alpha(1) -> 1(-)), where al is the highest fractional derivative order in the multi-term time ...
In this paper, we consider sharp pointwise-in-time error esti-mate of L1 scheme in time for solving the following nonlinear subdif f usion equations∂ αt u − ∆u = f(u),x ∈ Ω × (0,T] (1.1)with the initial and boundary conditionsu(x,0) = u 0 (x), x ∈ Ω,u...
Pointwise stabilization is proposed in this paper for a string equation where the observation signal is subject to a time delay. Different from the boundary control, the feedback stabilizer is acting at the middle joint of the string. Well-posedness of the open-loop system and solvability of th...
. this is a natural constraint since it models a volumetric restriction, which represents a limit to the total amount of control acting at any time t . this technological constraint is an alternative to pointwise or to energy constraints which have been considered previously in the literature. ...
pointwisein- time error estimatemaximal regularityIn this work we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation that involves a fractional derivative of order $\\alpha \\in (0,1)$ in ...
Pointwise-in-time α-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable coeffcientsdoi:10.3934/cam.2024003CAPUTO fractional derivativesTRANSPORT equationEQUATIONSIn this paper, a fully-discrete alternating direction implicit (ADI)...
For time-fractional parabolic equations with a Caputo time derivative of order \\alpha\\in(0,1) \\alpha\\in(0,1) , we give pointwise-in-time a posteriori error bounds in the spatial L_2 L_2 and L_\\infty L_\\infty norms. Hence, an adaptive mesh construction algorithm is applied ...
(DFGI).After that,we obtain the pointwise-in-time error estimate of the widely used L1 scheme for nonlinear subdiffusion equations.The present results fill the gap on some interesting convergence results of L1 scheme onσ∈(0,α)∪(α,1)∪(1,2].Numerical experiments are provided to ...
The gain governors use receding horizon optimization to adjust parameters (such as gains) in the nominal control laws. The parameters are optimized at each time instant to minimize a cost function subject to pointwise-in-time constraints and subject to the condition that the parameter values are ...
P.Cizek,W.Hardle,V.Spokoiny.Adaptive pointwise estimation in time-inhomogeneous time-series models.Center Discussion Paper Series35. 2007CIZEK, P., W. HARDLE, AND V. SPOKOINY (2007): "Adaptive Pointwise Estimation in Time- Inhomogeneous Time Series Models," Technical Report, Weierstrass ...