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Numerical Experiments
In this part, we discuss the results of our numerical tests. The code is based on Python 3.11. It is available for download from the last author’s...
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Numerical Differentiation
What is Numerical Differentiation? Numerical Differentiation is the approximation of the derivative of a...
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Numerical Integration
What is numerical integration? Numerical integration or (numerical) quadrature...
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Numerical Integration
Does our multilevel refinement work well? Does it approximate well the original domain? To check on this, we use numerical integration. Fortunately,...
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Numerical Multiscale Methods for Waves in High-Contrast Media
Multiscale high-contrast media can cause astonishing wave propagation phenomena through resonance effects. For instance, waves could be exponentially...
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Weighted numerical range and weighted numerical radius for even-order tensor via Einstein product
The main aim of this article is to introduce the weighted numerical range and the weighted numerical radius for an even-order square tensor via the...
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Modeling and Illustrative Numerical Examples
In this chapter, we present numerical examples of stochastic programming instances to illustrate the different models presented in Chap....
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Geometric Numerical Integration
Modern Numerical Analysis is not only devoted to approximating the solutions of various problems through accurate and efficient numerical schemes,...
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Harmonic Measures and Numerical Computation of Cauchy Problems for Laplace Equations
It is well known that the Cauchy problem for Laplace equations is an ill-posed problem in Hadamard’s sense. Small deviations in Cauchy data may lead...
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Conditionally Eulerian–Lagrangian Method on the Example of the Problem on the Dynamics of an Intrathermocline Vortex Lens
AbstractA new conditionally Eulerian–Lagrangian numerical method is developed to solve a number of problems in which the object of study is...
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Numerical Analysis
To illustrate results, this chapter introduces an academic as well as a very simplified insurance specific setup. The academic setup allows a...
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Numerical-Analytical Decomposition-Autocompensation Method for Signal Recognition from Incorrect Observations
AbstractA numerical-analytical method is developed for solving the problem of optimal recognition of a set of possible signals observed in the form...
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High Resolution Well-Balanced Compact Implicit Numerical Scheme for Numerical Solution of the Shallow Water Equations
In this work, we solve the shallow water equations with topography using a novel high resolution well-balanced compact implicit finite difference...
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Numerical Methods for Complex Interface Evolutions
In this chapter we focus on the numerical aspects of complex interface problems. First, the two major approaches, interface capturing and interface...
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Numerical Ranges of Antilinear Operators
We study numerical ranges of antilinear operators on both Hilbert and Banach spaces. We prove that the numerical range of an antilinear operator on...
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Influence of Numerical Diffusion on the Growth Rate of Viscous Fingers in the Numerical Implementation of the Peaceman Model by the Finite Volume Method
A numerical model of oil displacement by a mixture of water and polymer based on the Peaceman model is considered. Numerical experiments were carried...
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Some numerical radius bounds
In this paper, we first give two new upper bounds for the numerical radius of the product of two Hilbert space operators. The obtained bounds are...
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Implementation of Numerical Experiments
The last chapter is dedicated to the numerical experiments to verify our theoretical results obtained in this monograph, particularly in Chaps....
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Simulation of Vortex Interaction with a Shock Wave for Testing Numerical Algorithms
AbstractThe results of numerical simulation of the problem of the interaction of a vortex flow with a shock wave are presented on the example of...
