Pointwise-in-time α-robust error estimate of the ADI difference scheme for three-dimensional fractional subdiffusion equations with variable doi:10.3934/cam.2024003L1 schemethree-dimensional fractional equationADI schemevariable coefficientα-Robuststability and convergenceIn this paper, a fully-discrete ...
Meanwhile, a sharp pointwise-in-time error analysis is developed. In particular, the deriving convergent result implies that the error away from the initial time reaches the optimal convergence rate of 2 伪 / 2 by merely taking the grading parameter r = 1 for any 1 < 伪 < 2 . Finally,...
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...
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 ...
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 ...
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 time. The fully...
(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 ...
Using a novel discrete fractional Grnwall inequality, we obtain pointwise-in-time error estimates of the time-stepping methods. It is proved that as \\(tightarrow 0\\) , the convergence orders can be \\(\\sigma _{k}\\) , where \\(\\sigma _{k}\\) is the regularity parameter. ...
Spokoiny (2009) Adaptive pointwise estimation in time-inhomogeneous conditional heteroscedasticity models. The Econometrics Journal 12, 248-271.CIZEK, P., W. HARDLE, AND V. SPOKOINY (2007): "Adaptive Pointwise Estimation in Time- Inhomogeneous Time Series Models," Technical Report, Weierstrass ...