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The paper discusses the nonlinear behavior of a viscoelastic 3D thin film in frictional contact with a flat substrate. The frictional contact is modeled by Coulomb's law of friction at substrate. A function is included for damage caused by strain or excessive film stress to which the materials may be subjected over time. Assumptions and a functional framework are identified to allow for the existence and uniqueness of the weak solution to the problem. In contrast, preliminary estimates of the potential damage and stresses to the system during a specified operating period T are disclosed, the study concluded in the latter by an asymptotic analysis model of the problem explained with mathematical justifications and intended results. [ABSTRACT FROM AUTHOR]

The SIR (Susceptible–Infected–Removed) is one of the simplest models for epidemic outbreaks. The present paper derives a novel, simple, analytical asymptotic solution for the I-variable, which is valid on the entire real line. Connections with the Gompertz and Gumbel distributions are also demonstrated. The approach is applied to the ongoing coronavirus disease 2019 (COVID-19) pandemic in four European countries — Belgium, Italy, Sweden, and Bulgaria. The reported raw incidence data from the outbreaks in 2020–2021 have been fitted using constrained least squares. It is demonstrated that the asymptotic solution can be used successfully for parametric estimation either in stand-alone mode or as a preliminary step in the parametric estimation using numerical inversion of the exact parametric solution. [ABSTRACT FROM AUTHOR]

We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential equations, we derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model. The asymptotic convergence of the method is proved under appropriate regularity conditions, and a multi-stage method for improving the quality of the approximation is discussed. Numerical examples are also provided. [ABSTRACT FROM AUTHOR]

A new second-order two-scale (SOTS) asymptotic analysis method is presented for the heat conduction problems concerning composite materials with periodic configuration under the coordinate transformation. The heat conduction problems are solved on the transformed regular domain with quasi-periodic structure in the general curvilinear coordinate system. By the asymptotic expansion, the cell problems, effective material coefficients and homogenized heat conduction problems are obtained successively. The main characteristic of the approximate model is that each cell problem defined on the microscopic cell domain is associated with the macroscopic coordinate. The error estimation of the asymptotic analysis method is established on some regularity hypothesis. Some common coordinate transformations are discussed and the reduced SOTS solutions are presented. Especially by considering the general one-dimensional problem, the explicit expressions of the SOTS solutions are derived and stronger error estimation is presented. Finally, the corresponding finite element algorithms are presented and numerical results are analyzed. The numerical errors presented agree well with the theoretical prediction, which demonstrate the effectiveness of the second-order asymptotic analysis method. By the coordinate transformation, the asymptotic analysis method can be extended to more general domain with periodic microscopic structures. [ABSTRACT FROM AUTHOR]

Abstract: The time-dependent Vlasov–Maxwell equations are one of the most complete mathematical equations that model charged particle beams or plasma physics problems. However, the numerical solution of this system often requires a large computational effort. It is worthwhile, whenever possible, to take into account the geometrical or physical particularities of the problem to derive asymptotic simpler approximate models, leading to cheaper simulations. In this paper, we consider the case of high energy short beams, as for example the transport of a bunch of highly relativistic charged particles in the interior of a perfectly conducting hollow tube. We then derive and analyze a new paraxial asymptotic model, that approximates the Vlasov–Maxwell equations and is fourth order accurate with respect to a small parameter which reflects the physical characteristics of the problem. This approach promises to be very powerful in its ability to get an accurate and fast algorithm, easy to be developed. [Copyright &y& Elsevier]

In this article, a Gaussian quadrature rule was developed for the approximation of Fourier-type highly oscillatory integrals (FHOIs) with the phase functions of form g (x) = x r , r = 2 s , s ≥ 1 , x ∈ [ − 1 , 1 ]. The presence of these rules was demonstrated numerically through an analytical-numerical process, and questions were also addressed regarding the number of the nodes of the quadrature rule tend to the endpoints ± 1 and the number of those tend to the so-called stationary points (where the integrand does not oscillate locally) as ω → ∞. With proper assumptions, an asymptotic order was obtained for the numerical method, which indicated that the quadrature error decreased rapidly with the increase in oscillation parameter ω or the quadrature points. Furthermore, the behavior of the quadrature nodes as ω → ∞ and ω → 0 was analyzed to demonstrate the optimal asymptotic order and optimal polynomial order of the proposed method. To illustrate the efficiency and accuracy of the proposed method, some numerical examples were considered as well. In addition, the proposed method was compared to other numerical methods. [ABSTRACT FROM AUTHOR]

An external barrier option has a random variable which determines whether the option is knock-in or knock-out. In this paper, we deal with the pricing of the external barrier option under a stochastic volatility model incorporated by a fast mean-reverting process. By using a singular perturbation method (asymptotic analysis) on the given partial differential equation for the option price, and applying the double Mellin transform technique and the method of images, we derive the corrected option price, which is an explicit analytical approximated solution for the external barrier option. For numerical experiments, we verify the price accuracy of the external barrier option with a stochastic volatility model by comparing the approximated option price with the option price obtained by Monte Carlo simulation. Finally, we investigate the behavior and sensitivity of option prices to model parameters. [ABSTRACT FROM AUTHOR]

Abstract: In the context of simulation of electromagnetic propagation, the thin wire formalism of Holland and Simpson allows one to deal with scattering by perfectly conducting thin wires by coupling a standard FDTD method with a discrete 1D wave equation ruling the current inside the wires. This method can be very accurate, but it involves a fitting parameter that requires careful calibration. We propose a consistency analysis and derive a formula for the calibration of this parameter in the case of a simplified 2D analogue of the method of Holland and Simpson. Our proof relies on the observation that this method is actually a hidden version of the singular function method well known in the context of elliptic equations in domains with a singular boundary. [Copyright &y& Elsevier]

Abstract: We investigate a flow problem of relevance in bioremediation and develop a mathematical model for transport of contamination by groundwater and the spreading, confinement, and remediation of chemical waste. The model is based on the fluid mass and momentum balance equations and simultaneous transport and consumption of the pollutant (hydrocarbon) and nutrient (oxygen). Particular emphasis is placed on the study of processes involving the full coupling of reaction, transport and mechanical effects. Dimensional analysis and asymptotic reduction are used to simplify the governing equations, which are then solved numerically. [Copyright &y& Elsevier]

Abstract: The periodically forced extended KdVB (eKdVB) equation, which contains both KdVB and modified KdVB (mKdVB) equations as special cases, is known to possess a rich array of resonant steady solutions. We present an analytic methodology based on singular perturbation and asymptotic matching in order to illustrate and approximate these solutions in the limit that the dispersive effects are small relative to the nonlinear and forcing terms. Weak Burgers damping is also included at the same order as dispersion. Solutions across the resonant band may be constructed and show good agreement with solutions of the full equation, showing clearly the role of the various physical effects. In this way, direct comparisons and connections are made between the various classes of KdVB equations, illustrating, in particular, the underlying mathematical connections between the KdVB and mKdVB equations. [Copyright &y& Elsevier]

Abstract: Several three-term recurrence relations for confluent hypergeometric functions are analyzed from a numerical point of view. Minimal and dominant solutions for complex values of the variable are given, derived from asymptotic estimates of the Whittaker functions with large parameters. The Laguerre polynomials and the regular Coulomb wave functions are studied as particular cases, with numerical examples of their computation. [Copyright &y& Elsevier]

Abstract: Finite differences of values of the Riemann zeta function at the integers are explored. Such quantities, which occur as coefficients in Newton series representations, have surfaced in works of Bombieri–Lagarias, Maślanka, Coffey, Báez-Duarte, Voros and others. We apply the theory of Nörlund–Rice integrals in conjunction with the saddle-point method and derive precise asymptotic estimates. The method extends to Dirichlet L-functions and our estimates appear to be partly related to earlier investigations surrounding Li''s criterion for the Riemann hypothesis. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the asymptotic analysis of a minimizer of an n-Ginzburg–Landau-type functional. When the dimension , the asymptotic properties were well studied, such as the convergence of the minimum of the energy, the behavior of the minimizer near its zero points, and the quantization effects for the Euler–Lagrange system in . The author investigates those properties when the dimension n is not less than 3. [Copyright &y& Elsevier]

Abstract: We consider RCMS, a method for integrating differential equations of the form with highly oscillatory solution. It is shown analytically and numerically that RCMS can accurately integrate problems using stepsizes determined only by the characteristic scales of , typically much larger than the solution “wavelength”. In fact, for a given grid the error decays with, or is independent of, increasing solution oscillation. RCMS consists of two basic steps, a transformation which we call the right correction and solution of the right correction equation using a Magnus series. With suitable methods of approximating the highly oscillatory integrals appearing therein, RCMS has high order of accuracy with little computational work. Moreover, RCMS respects evolution on a Lie group. We illustrate with application to the 1D Schrödinger equation and to Frenet–Serret equations. The concept of right correction integral series schemes is suggested and right correction Neumann schemes are discussed. Asymptotic analysis for a large class of ODEs is included which gives certain numerical integrators converging to exact asymptotic behaviour. [Copyright &y& Elsevier]

A general relaxation system which yields compressible and incompressible Euler and Navier–Stokes equations in the limit is presented. Such a system can be used to set up relaxation schemes that work uniformly in the above limits. A higher order nonoscillatory upwind spatial discretization and TVD implicit–explicit method for time integration are considered. Numerical computations are carried out on various test problems. [Copyright &y& Elsevier]

In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Navier–Stokes equation. The kinetic equation is discretized with a first- and second-order discretization in space. The discretized equation is then considered in the low Mach number limit. Using this limit a second-order discretization for the convective part in the incompressible Navier–Stokes equation is obtained. Numerical experiments are shown comparing different approaches. [Copyright &y& Elsevier]

In this paper, we consider the problem of pricing a variance swap whose underlying asset price dynamics is modeled under a hybrid framework of constant elasticity of variance and stochastic volatility (SVCEV). Applying the multi-scale asymptotic analysis approach, we obtain a semi-closed form approximation of the fair continuous variance strike. We conduct numerical experiments by applying this approximation formula to calculate the square root of the fair continuous variance strike with different values of parameters. The market data of S&P 500 options are used to obtain calibrations of the SVCEV model, and then the estimated parameters are further used to compute the values of the square root of fair continuous variance strike. In addition, we also analyze and compare the performance of the CEV model, the SVCEV model and the Heston stochastic volatility model. [ABSTRACT FROM AUTHOR]

In this paper, we construct approximations of the microscopic solution of a nonlinear reaction–diffusion equation in a domain consisting of two bulk-domains, which are separated by a thin layer with a periodic heterogeneous structure. The size of the heterogeneities and thickness of the layer are of order ϵ , where the parameter ϵ is small compared to the length scale of the whole domain. In the limit ϵ → 0 , when the thin layer reduces to an interface Σ separating two bulk domains, a macroscopic model with effective interface conditions across Σ is obtained. Our approximations are obtained by adding corrector terms to the macroscopic solution, which take into account the oscillations in the thin layer and the coupling conditions between the layer and the bulk domains. To validate these approximations, we prove error estimates with respect to ϵ. Our approximations are constructed in two steps leading to error estimates of order ϵ 1 2 and ϵ in the H 1 -norm. [ABSTRACT FROM AUTHOR]