Optimal error estimates of spectral Petrov-Galerkin and collocation methods for initial value problems of fractional differential equations [PDF]
, 2015 We present optimal error estimates for spectral Petrov-Galerkin methods and spectral collocation methods for linear fractional ordinary differential equations with initial value on a finite interval.
Zeng, F., Zhang, Z., Em Karniadakis, G.
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Estimates of convolutions of certain number-theoretic error terms
International Journal of Mathematics and Mathematical Sciences, 2004 Several estimates for the convolution function C [f(x)]:=∫1xf(y) f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number-theoretic error term.
Aleksandar Ivic
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A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations
Journal of Inequalities and Applications, 2016 In this paper, we provide a new type of study approach for the two-dimensional (2D) Sobolev equations. We first establish a semi-discrete Crank-Nicolson (CN) formulation with second-order accuracy about time for the 2D Sobolev equations. Then we directly
Zhendong Luo
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Generalized Beta Prime Distribution Applied to Finite Element Error Approximation
Axioms, 2022 In this paper, we propose a new family of probability laws based on the Generalized Beta Prime distribution to evaluate the relative accuracy between two Lagrange finite elements Pk1 and Pk2 ...
Joël Chaskalovic, Franck Assous
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Accurate error estimation in CG [PDF]
Numerical Algorithms, 2021 In practical computations, the (preconditioned) conjugate gradient (P)CG method is the iterative method of choice for solving systems of linear algebraic equations $Ax=b$ with a real symmetric positive definite matrix $A$. During the iterations it is important to monitor the quality of the approximate solution $x_k$ so that the process could be stopped
Gérard Meurant, Jan Papez, Petr Tichý
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Measurement error in time-series analysis: a simulation study comparing modelled and monitored data. [PDF]
, 2013 BACKGROUND: Assessing health effects from background exposure to air pollution is often hampered by the sparseness of pollution monitoring networks. However, regional atmospheric chemistry-transport models (CTMs) can provide pollution data with national ...
Richard W Atkinson +25 more
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A priori error estimates for optimal control problems with pointwise constraints on the gradient of the state [PDF]
, 2011 We analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable. We derive convergence rates if the control space is discretized implicitly by the state equation. In contrast to
Ortner, Christoph +4 more
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Quantum Calculus-Based Error Estimations in Hermite-Hadamard Type Inequalities [PDF]
Sahand Communications in Mathematical AnalysisThe main aim of this article is to present error approximations for Hermite-Hadamard inequalities, which are connected with $_{\omega_{1}}\mathfrak{q}$-fractional calculus operators and are based on $\mathrm{(\rho, m)}$-convex functions.
Muhammad Samraiz +3 more
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A Comparative Study on the Estimation of the Parameters of the Markovian Processes- II [PDF]
The Egyptian Statistical Journal, 1983 Consider the stationary autoregressive process with order one and non-zero mean. The weight parameter is taken to be priori distributed as uniform, standard normal and normal with zero mean. The Bayes' estimates are obtained and compared with conditional
A.A. Abd-Alla, A.M. Abouammoh
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Numerical validation of probabilistic laws to evaluate finite element error estimates
Mathematical Modelling and Analysis, 2021 We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m).
Jöel Chaskalovic, Franck Assous
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