Efficient approximation of random fields for numerical applications [PDF]
, 2014 This article is dedicated to the rapid computation of separable expansions for the approximation of random fields. We consider approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky ...
Michael Peters +5 more
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Generating Numerical Approximations
Computational Linguistics, 2012 We describe a computational model for planning phrases like “more than a quarter” and “25.9 per cent” which describe proportions at different levels of precision. The model lays out the key choices in planning a numerical description, using formal definitions of mathematical form (e.g., the distinction between fractions and percentages) and roundness ...
Richard Power, Sandra Williams
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Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes [PDF]
, 2010 A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the ...
Rüdiger Müller +11 more
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Numerical Approaches to Fractional Integrals and Derivatives: A Review
Mathematics, 2020 Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality—has attracted increasing interest due to its potential applications in the real world.
Min Cai, Changpin Li
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Numerical Ruin Probability in the Dual Risk Model with Risk-Free Investments
Risks, 2018 In this paper, a dual risk model under constant force of interest is considered. The ruin probability in this model is shown to satisfy an integro-differential equation, which can then be written as an integral equation. Using the collocation method, the
Sooie-Hoe Loke, Enrique Thomann
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Local RBF approximation for scattered data fitting with bivariate splines [PDF]
, 2005 In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm.
Oleg Davydov +5 more
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Accurate ENO-like schemes for the model of fluid flows in a nozzle with variable cross-section [PDF]
Iranian Journal of Numerical Analysis and OptimizationA class of accurate high-order $ENO$-like schemes for the model of fluid flows in a nozzle with variable cross-section is presented. The model contains a nonconservative source term, which causes unsatisfactory results to standard numerical schemes, even
D.H. Cuong, M.D. Thanh
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Numerical Approximation of Optimal Convex Shapes [PDF]
SIAM Journal on Scientific Computing, 2020 This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem. Moreover, we prove the convergence of discretizations in two-dimensional situations. A numerical algorithm is devised
Sören Bartels, Gerd Wachsmuth
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Finite element approximation of a nonlinear cross-diffusion population model [PDF]
, 2003 We consider a fully discrete finite element approximation of the nonlinear cross-diffusion population model: Find u i, the population of the ith species, i = 1 and 2, such that ∂ui ∂t −Δ [ ci ui + ai u2i + ui uj] − bi ∇.
John W. Barrett +6 more
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Optimal Control of the Van der Pol Oscillator Problem by Using Orthogonal Polynomial-Based Optimization [PDF]
Control and Optimization in Applied MathematicsThe orthogonal polynomials approximation method is widely regarded as a highly effective and versatile technique for solving optimal control problems in nonlinear systems.
Reza Dehghan
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