We consider a nonlinear singularly perturbed Volterra integro-differential equation. The problem is discretized by an implicit finite difference scheme on an arbitrary non-uniform mesh. The scheme comprises of an implicit difference operator for the derivative term and an appropriate quadrature rule for the integral term. We establish both a priori and a posteriori error estimates for the scheme that

In this paper we introduce a new integer valued autoregressive model of order one. The specificity of this model is based on its non-linear structure. The autoregressive component is defined through the binomial thinning operator. Also, an additional process is introduced into the autoregressive component. This random process controls how the previous value influences the next value of the observed

In this note, we examine the performance of 25 new composite models that are derived from 5 underlying folded distributions for modeling insurance loss data. These models are assessed using standard selection criteria involving the Akaike Information Criteria and the Bayesian Information Criteria as well as proximity to empirical risk estimates. Three models are found significant in improving the goodness-of-fit

The test of independence of two groups of variables is addressed in the case where the sample size N is considered randomly distributed. This assumption may lead to a more realist testing procedure since in many situations the sample size is not known in advance. Three sample schemes are considered where N may have a Poisson, Binomial or Hypergeometric distribution. For the case of two groups with

This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control.

The Quantum Approximate Optimization Algorithm (QAOA) was proposed as a way of finding good, approximate solutions to hard combinatorial optimization problems. QAOA uses a hybrid approach. A parametrized quantum state is repeatedly prepared and measured on a quantum computer to estimate its average energy. Then, a classical optimizer, running in a classical computer, uses such information to decide

Implicit schemes for solving large-scale linear differential–algebraic systems with constant coefficients necessitate at each integration step the solution of a linear system, typically obtained by a Krylov subspace method such as GMRES. To accelerate the convergence, an approach is proposed that computes good initial guesses for each linear system to be solved in the implicit scheme. This approach

A computational hydrodynamic model of interacting galaxies is presented. The interstellar medium (ISM) is described by a model of gravitational multicomponent single-velocity hydrodynamics. A model based on first moments of the collisionless Boltzmann equation is used to describe the stellar component and dark matter. Subgrid processes of star formation and supernovae feedback, as well as cooling and

Stability is a basic property of dynamical systems. In this paper we analyze the stability of multidimensional systems and present new sufficient conditions for the asymptotic stability in terms of linear matrix inequalities. We treat both the discrete-time and continuous-time cases and also propose variants that require linear matrix inequalities of more moderate size.

In this work, a matrix Riemann-Hilbert problem of a mixed Chen-Lee-Liu derivative nonlinear Schrödinger (CLL-NLS in brief) equation on the half-line is established by the unified transformation approach. the solution satisfying an initial–boundary value data of the CLL-NLS equation is reconstructed by solving the matrix Riemann-Hilbert problem. Especially, the spectral functions are not independent

Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure of association. These bounds have been computed for Spearman’s rho, Kendall’s tau, and Blomqvist’s beta. The importance of another two measures of association, Spearman’s

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the

The constant elasticity of variance (CEV) model is a practical approach to option pricing by fitting to the implied volatility smile. However, pricing American options is computationally intensive because no analytical formulas are available. In this paper, we present numerical methods to find the optimal exercise boundary with respect to an American put option under the CEV model. This problem corresponds

We develop a practical discrete model of hysteresis based on nonlinear play and generalized play, for use in first-order conservation laws with applications to adsorption–desorption hysteresis models. The model is easy to calibrate from sparse data, and offers rich secondary curves. We compare it with discrete regularized Preisach models. We also prove well-posedness and numerical stability of the

Riccati differential equations arise in many different areas and are particularly important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff Riccati differential equations. We show how to apply exponential Rosenbrock-type integrators to get approximate solutions. Two typical exponential integration schemes are considered. The implementation

Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional H1-norm analysis (corresponding to the case for a classical diffusion equation) to the time approximations of a fractional subdiffusion problem always leads to suboptimal error estimates (a loss of time accuracy). To recover the theoretical accuracy in time, we

The objective function in the nonsmooth optimization model of the clusterwise linear regression (CLR) problem with the squared regression error is represented as a difference of two convex functions. Then using the difference of convex algorithm (DCA) approach the CLR problem is replaced by the sequence of smooth unconstrained optimization subproblems. A new algorithm based on the DCA and the incremental

We investigate a nonconvex, nonsmooth optimization approach based on DC (Difference of Convex functions) programming and DCA (DC Algorithm) for the so-called DC fitting problem, which aims to fit a given set of data points by a DC function. The problem is tackled as minimizing the squared Euclidean norm fitting error. It is formulated as a DC program for which a standard DCA scheme is developed. Furthermore

In this paper, we present a constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for solving a linear stochastic parabolic partial differential equation driven by additive noises. When the diffusion coefficient in the stochastic parabolic partial differential equation varies in multiple scales, it is very challenging to resolve all scales for the model using traditional

In this paper, we consider the numerical approximation of stochastic partial differential equations driven by infinite dimensional fractional Brownian motion with Hurst index H>12. A Fourier spectral collocation approximation is used in space and semi-implicit Euler method is applied for the temporal approximation. Our aim is to investigate the convergence of the proposed method. Optimal strong convergence

This paper considers the numerical approximation of a two-component phase-field crystal model consisting of two coupled nonlinear Cahn-Hilliard equations of binary alloys. We develop a highly efficient time-marching scheme with second-order accuracy based on the SAV approach, in which two additional stabilization terms are introduced to improve stability, thus allowing large time steps. Unconditional

Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome this computational challenge, various multiscale methods are developed. In this paper, we consider a class of linear poroelasticity problems in high contrast heterogeneous

We propose an incremental aggregated proximal alternating direction method of multipliers (IAPADMM) for solving a class of nonconvex optimization problems with linear constraints. The new method inherits the advantages of the classical alternating direction method of multipliers and the incremental aggregated proximal method, which have been well studied for structured optimization problems. With some

This paper compares the performance of seven different element agglomeration algorithms on unstructured triangular/tetrahedral meshes when used as part of a geometric multigrid. Five of these algorithms come from the literature on AMGe multigrid and mesh partitioning methods. The resulting multigrid schemes are tested matrix-free on two problems in 2D and 3D taken from radiation transport applications;

This paper considers an approximate factorisation of three bivariate Bernstein basis polynomials that are defined in a triangular domain. This problem is important for the computation of the intersection points of curves in computer-aided design systems, and it reduces to the determination of an approximate greatest common divisor (AGCD) d(y) of the polynomials. The Sylvester matrix and its subresultant

We study the relative error in the numerical integration of the long-time solution of a linear ordinary differential equation y′(t)=Ay(t),t≥0, where A is a normal matrix. The numerical long-time solution is obtained by using at any step an approximation of the matrix exponential. This paper analyzes the relative error in the stiff situation and it shows that, in this situation, some A-stable approximants

The order statistics (OSs) arise in both practical and theoretical aspects including goodness-of-fit tests, characterizations of probability distributions and some estimation approaches such as the L-moments method. Most of these instances are connected with moments of OSs. The records and k-record statistics, also called kth record values in the literature, are other important topics related to the

This article presents an error analysis of the symmetric linear/bilinear partially penalized immersed finite element (PPIFE) methods for interface problems of Helmholtz equations. Under the assumption that the exact solution possesses a usual piecewise H2 regularity, the optimal error bounds for the PPIFE solutions are derived in an energy norm and the usual L2 norm. A numerical example is conducted

In this paper, we consider the incompressible Stokes flow problem in a perforated domain and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method provides a flexible and systematical approach to construct crucial divergence-free multiscale basis functions for approximating the velocity field. These basis functions

Hierarchical B-splines that allow local refinement have become a promising tool for developing adaptive isogeometric methods. Unfortunately, similar to tensor-product B-splines, the computational cost required for assembling the system matrices in isogeometric analysis with hierarchical B-splines is also high, particularly if the spline degree is increased. To address this issue, we propose an efficient

This paper proposes an alternative estimation method for cointegration, which allows for variation in the leads and lags in the cointegration relation. The method is more powerful than a standard method. Illustrations to annual inflation rates for Japan and the USA and to seasonal cointegration for quarterly consumption and income in Japan shows its ease of use and empirical merits.

In this paper, we propose a second-order finite difference scheme to study a class of space–time variable-order fractional diffusion equation, and show that the scheme is not only unconditionally stable but also convergent with the convergence order O(τ2+h2) under certain conditions. Some numerical examples are illustrated which are in good agreement with our theoretical results.

In this paper, we define the mixed fractional Constant Elasticity of Variance (CEV) process exploiting a transfer equation. This transformation enables us to shift non-linearity from the volatility coefficient into the drift one and accordingly, the problem can be more easily studied. We confirm the existence of a unique positive solution to the transfer equation and verify the conditions under which

Insurance contracts pricing, that is determining the risk loading added to the expected loss, plays a fundamental role in insurance business. It covers the loss from adverse claim experience and generates a profit. As market competition is a key component in the pricing exercise, this paper proposes a novel dynamic pricing game model with multiple insurers who are competing with each other to sell

A time-fractional initial–boundary problem is considered on a bounded spatial domain Ω⊂Rd, where d∈{1,2,3} and Ω is convex or smooth. The differential equation is ∑i=1lqiDtαiu(x,t)−Δu(x,t)=f, where each Dtαi is a Caputo derivative with 0<αl<⋯<α1<1 and the qi are positive constants. A new error analysis is given for the numerical method (L1 scheme in time, finite elements in space) of Huang and Stynes

In this paper, we investigate an inverse eigenvalue problem for matrices that are obtained from pseudo-Jacobi matrices by only modifying the (1,r)-th and (r,1)-th entries, 3≤r≤n. Necessary and sufficient conditions under which the problem is solvable are derived. Uniqueness results are presented and an algorithm to reconstruct the matrices from the given spectral data is proposed. Illustrative examples

This paper discusses a class of two-block nonconvex smooth optimization problems with nonlinear constraints. Based on a quadratically constrained quadratic programming (QCQP) approximation, an augmented Lagrangian function (ALF), and a Lagrangian splitting technique into small-scale subproblems, we propose a novel sequential quadratic programming (SQP) algorithm. First, inspired by the augmented Lagrangian

In this paper, we develop a new upwind weak Galerkin finite element scheme for linear hyperbolic equations. The upwind-type stabilizer is imposed in the scheme. An error estimate is investigated for a suitable norm. Finally, numerical examples are presented for validating the theoretical conclusions.

Computational aerodynamic analyses of rotorcraft main rotor blades are performed in both hover and forward flight. The open-source SU2 code is used for rotor performance prediction. The core of the code is the set of RANS equations, which are solved for determining the flow. In hover, both steady-state and time-accurate modelling techniques of varying complexity are used and assessed. Simulation specific

In this article, a new recovery method is designed and analyzed for curl conforming elements on cuboid mesh. The proposed recovery method fully exploits the potential of symmetry to obtain the superconvergence of recovered edge finite element solution in discrete ℓ2 norm. The idea is to identify a symmetry sub-domain such that a polynomial of the same degree is recovered by local L2 projection, based

In this paper, we introduce novel discontinuous Galerkin (DG) schemes for the Cahn-Hilliard equation, which arises in many applications. The method is designed by integrating the mixed DG method for the spatial discretization with the Invariant Energy Quadratization (IEQ) approach for the time discretization. Coupled with a spatial projection, the resulting IEQ-DG schemes are shown to be unconditionally

We propose a non-intrusive reduced-oder modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides an optimally ordered basis from a set of selected full-order snapshots. Truncating this optimal basis, we construct a reduced-order model with undetermined coefficients

In this paper, we mainly consider the velocity error analysis of H(div)-conforming DG method for the semi-discrete time-dependent Navier–Stokes equations. Firstly, we prove that the L∞(0,T;L2(Ω)) error of the velocity is optimal and pressure-robust, but the constants in the velocity error bound are dependent on the inverse power of the viscosity, so it is not semi-robust. Secondly, we focus on pressure-robust

A large number of researches addressed the problem of monitoring statistical processes using complete data. Nevertheless, in engineering applications, especially reliability engineering and lifetime test, we often observe the incomplete or censored sample. In this paper, we introduce three EWMA schemes for monitoring exponentially distributed processes based on type-II censored data. Our proposed procedure

In this work we study a thermoelastic problem involving binary mixtures. Type III thermal theory is considered for the modeling of the heat conduction. Existence, uniqueness and continuous dependence of solutions are proved by using the semigroup theory. Then, the numerical analysis of the resulting variational problem is considered, by using the finite element method for the spatial approximation

The mathematical modeling of various real life applications leads to systems of ordinary differential equations which include crucial properties like the positivity of the solution as well as the conservation of mass or energy. Based on the fundamental work of Burchard et al. (2003), unconditionally positive and conservative modified Patankar–Runge–Kutta schemes (MPRK) are available. These methods

The work is devoted to algorithms for solving high-temperature gas dynamics problems on high-performance computing systems. Energy transfer by radiation is described in the approximation of radiative heat conduction. The algorithm is based on the hyperbolic model of thermal conductivity, which can significantly increase the stability of explicit schemes. Examples of numerical calculations are presented

The determination of exponentially stable equilibria and their basin of attraction for a dynamical system given by a general autonomous ordinary differential equation can be achieved by means of a contraction metric. A contraction metric is a Riemannian metric with respect to which the distance between adjacent solutions decreases as time increases. The Riemannian metric can be expressed by a matrix-valued

The topology of Arnold-Liouville level sets of the real forms of the complex generic Neumann system depends indirectly on the positions of the roots of the special polynomial US(λ). For certain polynomials, the existence and positions of the real roots, according to the suitable parameters of the system, is not obvious. In the paper, a method for checking the existence and positions of the real roots

In the paper, we study two-dimensional nonlinear spatial fractional complex Ginzburg–Landau equations. A centered finite difference method is exploited to discretize the spatial variables, while a three-level finite difference scheme is applied for the time integration. Theoretically, we prove the proposed method is uniquely solvable and unconditionally stable, with second order accuracy on both time

While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case of unilateral rapidly decreasing functions. To address this issue, Stenger proposed the application of a conformal map to the integrand such that it transforms into bilateral rapidly decreasing functions. Okayama and Hanada

In this paper, we consider the numerical solution of a model problem in the form of a parabolic hemivariational inequality that arises in applications of semipermeable media. The model problem is first studied as a particular case of an abstract parabolic hemivariational inequality. A general fully discrete numerical method is introduced for the abstract parabolic hemivariational inequality, where

Stop-loss contracts are the most commonly used reinsurance agreements in insurance whose important factors are the retention and the maximum (cap) values attained on the random loss, which may occur within the policy period. Therefore, determining and forecasting the loss amounts is an important issue for both the insurer and the reinsurer. Along with many approaches in actuarial literature, we propose

An abstract framework of the virtual element method is established for solving general elliptic hemivariational inequalities with or without constraint, and a unified a priori error analysis is given for both cases. Then, virtual element methods of arbitrary order are applied to solve three elliptic hemivariational inequalities arising in contact mechanics, and optimal order error estimates are shown

In this paper a parabolic–parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the two-dimensional case. Several

In this paper, we present and analyze a new space–time ultra-weak discontinuous Galerkin (UWDG) finite element method for the second-order wave equation in one space dimension. The UWDG finite element approximations are used in space variable and also for the temporal approximation. The space–time UWDG discretization is presented in detail, including the definition of the numerical fluxes, which are

The advantages of the barycentric rational interpolation (BRI) introduced by Floater and Hormann include the stability of interpolation, no poles, and high accuracy for any sufficiently smooth function. In this paper we design a transformed BRI scheme to solve two dimensional fractional Volterra integral equation (2D-FVIE), whose solution may be non-smooth since its derivatives may be unbounded near

This paper is devoted to adaptive signal denoising in the context of Graph Signal Processing (GSP) using Spectral Graph Wavelet Transform (SGWT). This issue is addressed via a data-driven thresholding process in the transformed domain by optimizing the parameters in the sense of the Mean Square Error (MSE) using the Stein’s Unbiased Risk Estimator (SURE). The SGWT considered is built upon a partition

In this paper, several accelerating strategies for the numerical methods of topology optimization are proposed. In our implementation, the finite element method is used for discretization, and the novelty of this research lies in two aspects. Two different meshes with variable element sizes are used to discretize the state equation and the level-set evolution equation. On the other hand, GPU-based

In this paper, we consider numerical approximations for the modified phase field crystal model with long-range interaction, which describes the micro-phase separation in diblock copolymers. The model is a nonlinear damped wave equation with a nonlocal term that includes both diffusive dynamics and elastic interaction. To develop easy-to-implement time-stepping schemes with unconditional energy stabilities