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L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type

Ziwen Jiang (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in $ℝ^{2}$ , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation $u_{t} = div {a ▽ u + \int_{0}^{t} b_{1} ▽ u d τ + \int_{0}^{t} 𝐜 u d τ} + f$ based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...

Lp estimates of boundary integral equations for some nonlinear boundary value problems.

J. Saranen, P.P.B. Eggermont (1990/1991)

Numerische Mathematik

Matematika dokonale ukrytá v počítačové tomografii

Vítězslav Vít Vlček, Karel Segeth (2008)

Pokroky matematiky, fyziky a astronomie

Mathematical Aspects of 't Hooft's Eigenvalue Problem in Two-Dimensional Quantum Chromodynamcis Part III.

Stefan Hildebrandt (1979)

Mathematische Zeitschrift

Maximal monotone model with delay term of convolution.

Lamarque, Claude-Henri, Bastien, Jérôme, Holland, Matthieu (2005)

Mathematical Problems in Engineering

Midpoint collocation for Cauchy singular integral equations.

G.A. Chandler (1992)

Numerische Mathematik

Minimax and bayes estimation in deconvolution problem*

Mikhail Ermakov (2008)

ESAIM: Probability and Statistics

We consider a deconvolution problem of estimating a signal blurred with a random noise. The noise is assumed to be a stationary Gaussian process multiplied by a weight function function εh where h ∈ L2(R1) and ε is a small parameter. The underlying solution is assumed to be infinitely differentiable. For this model we find asymptotically minimax and Bayes estimators. In the case of solutions having finite number of derivatives similar results were obtained in [G.K. Golubev and R.Z. Khasminskii,...

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

More on the Weeks Method for the Numerical Inversion of the Laplace Transform.

G. Giunta, G. Laccetti, M.R. Rizzardi (1989)

Numerische Mathematik

Multichannel deblurring of digital images

Michal Šorel, Filip Šroubek, Jan Flusser (2011)

Kybernetika

Blur is a common problem that limits the effective resolution of many imaging systems. In this article, we give a general overview of methods that can be used to reduce the blur. This includes the classical multi-channel deconvolution problems as well as challenging extensions to spatially varying blur. The proposed methods are formulated as energy minimization problems with specific regularization terms on images and blurs. Experiments on real data illustrate very good and stable performance of...