Multimodal data are often present in synthetic aperture radar (SAR) image processing. Such images are often modeled by probability mixtures, but such solution may involve a large number of parameters and its inference becomes challenging. To address this issue, we proposed a probability distribution capable of describing multimodal data with only three parameters. The introduced model is defined by

We present a novel fast direct solver to simulate 3D large scale elastic inclusion problems. The method combines the isogeometric analysis boundary element method (IGABEM) and the hierarchical off-diagonal low-rank (HODLR) matrix based on non-uniform rational B-splines (NURBS). Hence the 3D geometric surface can be accurately described by the bivariate NURBS basis functions. In order to solve the large

In order to understand the environmental trend of network finance and the impact of network finance on traditional commercial banks, after analyzing the transaction risks of network finance, this study learns from the advanced models of credit risk measurement and early warning at home and abroad and the latest artificial intelligence technology, combining them with China’s national conditions, so

The surface of partial differential equation (PDE surface) is a surface that satisfies the PDE with boundary conditions, which can be applied in surface modeling and construction. In this paper, the construction of tensor product Bézier surfaces of triharmonic equation from different boundary conditions is presented. The internal control points of the resulting triharmonic Bézier surface can be obtained

In this paper, by integrating the Arnoldi method with the Chebyshev acceleration technique, we present the Arnoldi-Chebyshev method for computing the PageRank vector of the Google matrix. Convergence analysis of this method is exhibited. In addition, some numerical experiments are carried out to demonstrate the competitiveness of the new method with a few state-of-the art iterative methods.

In this paper, a sixth-kind Chebyshev collocation method will be considered for solving a class of variable order fractional nonlinear quadratic integro-differential equations (V-OFNQIDEs). The operational matrix of variable order fractional derivative for sixth-kind Chebyshev polynomials is derived and then, a collocation approach is employed to reduce the V-OFNQIDE to a system of nonlinear algebraic

We propose an extension of the hybrid difference method called the interface hybrid difference methods for solving elliptic interface equations. The hybrid difference method is composed of two types of approximations: one is the finite difference approximation of PDEs within cells (cell FD) and the other is the intercell finite difference (intercell FD) on edges of cells. The intercell finite difference

The finite difference preconditioning for higher-order compact scheme discretizations of non separable Poisson’s equation is investigated. An eigenvalue analysis of a one-dimensional problem is detailed for compact schemes up to the tenth-order. The analysis concludes that the spectrum is bounded irrespective of the mesh size and the continuous variable coefficient. Hence, combined to a multigrid method

In this paper, we have considered two classes of second-order balanced stochastic Runge–Kutta methods to multidimensional Itô stochastic differential equations. The control functions in the proposed methods are used to improve and enhance the convergence and stability properties of the method. The strong convergence of the second-order balanced stochastic Runge–Kutta methods is analyzed. The preservation

This paper considers an extension to the classical compound Poisson risk process by introducing a dependence structure between the inter-claim time and the claim size. We adopt the Spearman copula for constructing the dependence with the purpose of covering a wide range of positive dependence and developing a convex approximation to some bivariate copulas. We study the Laplace transform of the moments

We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the generalized condenser are bordered by piecewise smooth Jordan curves or are rectilinear slits. The presented method is used also to compute the harmonic measure in multiply

Interval arithmetic libraries provide the four elementary arithmetic operators for operand intervals bounded by floating-point numbers. Actual implementations need to make a large case analysis that considers, e.g., magnitude relations between all pairs of argument bounds, positional relations between the arguments and zero, and handling of the special values ±∞ and NaN. Their correctness is not obvious

This paper discusses an uncertain multi-period portfolio selection problem in the situation where the future security return rates are given by experts’ estimations instead of historical data. In financial market, investors may have different attitudes towards risk for different goals. In order to reflect these conflicting risk attitudes for different goals, mental accounts are introduced to the investment

We propose and numerically solve a new variational model for automatic saliency detection and segmentation in digital images. Using a non-local framework we consider a family of edge preserving functions combined with a new quadratic saliency detection term. Such a term defines a constrained bilateral obstacle problem for image classification driven by p-Laplacian operators, including the so-called

This paper is devoted to the study of a hemivariational inequality modeling the quasistatic bilateral frictional contact between a viscoelastic body and a rigid foundation. The damage effect is built into the model through a parabolic differential inclusion for the damage function. A solution existence and uniqueness result is commented. A fully discrete scheme is introduced with the time derivative

The backward problems for the elliptic equation (BPEE) are widely used for modelling problems in many fields such as physics, geometry or engineering. This paper is the first investigation of BPEE in unbounded multiple-dimensional domain associated with locally Lipschitz source as follows ∂2u∂x12+∂2u∂x22+...∂2u∂xn2+∂2u∂y2=S(x1,x2,…,xn,y,u(x1,x2,…,xn,y)),in which (x1,x2,…,xn,y)∈Rn×0,L, where L>0. Based

According to the well-known age replacement policy, the system is replaced preventively at time t or correctively at system failure, whichever occurs first. For a coherent system consisting of components having common failure time distribution which has increasing failure rate, we present necessary conditions for the existence of the unique optimal value which minimizes the mean cost rate. The conditions

In the present research article, we investigated the slip flow of an unsteady incompressible Oldroyd-B fluid model. The electroosmosis and the pressure gradient have been seized for the stimulation of flow. The progress of the fluid is treated to be as passage composed by two micro-parallel plates. The potential difference alive between hard surface and the fluid is taken to be non symmetric. The governing

In this paper, a general framework using tensor Krylov projection techniques is proposed for solving high order Sylvester tensor equations. After describing the tensor format of the generalized Hessenberg process, we combine the obtained different processes with a Galerkin orthogonality condition or with a minimal norm condition in order to derive the Hess−BTF and CMRH−BTF methods which are based on

We propose and analyze a linearly stabilized semi-implicit diffusive Crank–Nicolson scheme for the Cahn-Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic system with constant coefficients and provable discrete energy dissipation. Rigorous error analysis is carried out for the fully

In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reaction–diffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional)

A linear Multistep Block Hybrid Method with four off-grid points is presented for the direct approximation of the solution of fourth order Boundary Value Problems. Multiple Finite Difference formulas are derived and grouped into a unique block to form a numerical integrator to solve directly the fourth order problem, without the need to reduce it previously to a first-order system. The convergence

In the article R. Ferro and J.A. Virtanen (2017), the authors conjecture that δToep,∗(A)=δ(A), where A is a block Toeplitz matrices whose blocks have no specific structure. In this work we answer the correctness of the conjecture.

In this article we focus on option Greeks computation by means of Radial Basis Functions (RBF) with Partition of Unity methods. We start by presenting RBF applications to the financial world: we price single-underlying European and American barrier options and an American basket option on two correlated underlyings. Furthermore, we derive the expression for Greeks calculation via RBF and we compare

This paper primarily focuses on the distributions of the solutions for uncertain fractional difference equations by comparison theorems. First, comparison theorems are obtained for the fractional difference equations involving Riemann–Liouville type. Then the concepts of symmetrical uncertain variable and α-path to an uncertain fractional difference equation are introduced. Moreover, the relations

The main aim of this paper is to construct a new computational approach for the numerical solution of generalized Black–Scholes equation. In this approach, the temporal variable is discretized using Cranck-Nicolson scheme and spatial variable is discretized using sextic B-spline collocation method. Convergence analysis of the method is discussed. The proposed method is proved to be stable and have

The objective of this paper is to present a new Large Eddy Simulation (LES) model obtained by filtering a generalized version of the Navier–Stokes equations with nonlinear viscosity. This new model is a generalization of the model introduced in Rodríguez and Taboada-Vázquez (2017). The new LES model, in which viscosity has been substituted by a non linear function of the strain rate tensor, has been

A second-order hydrostatic reconstruction (HR) scheme for the shallow water equations with a non-flat bottom topography and a Manning friction is presented. The framework of our reconstruction was from Chen and Noelle (2017). We extend it from first-order to second-order accuracy. The new second-order HR scheme endows with a new implicit method, which is used to cope with the friction term, can exactly

In the method of fundamental solutions (MFS), source nodes on circles outside the solution domains S has been widely applied in numerical computation. In this paper, source nodes on an ellipse are proposed for solving Laplace’s equation using the MFS, and a robust error and stability analysis is established. Bounds on errors and condition numbers are derived for bounded simply-connected domains. Polynomial

In this paper we examine the possibility of using the Eta functions as a new base for high quality approximations of oscillatory functions with slowly varying weights. We focus on the least squares and piecewise least squares approximation of such functions and compare the results obtained by using Eta-based sets of functions with those obtained by means of the Legendre polynomials and Fourier series

In this work, we propose a new class of A-stable diagonally implicit four stage Runge–Kutta (R–K) methods with minimal dissipation and optimally low dispersion error. These schemes obtained by minimizing both amplification and phase error enjoy fourth order of accuracy and are suitable for stiff systems. Emphasis here is to outline an algorithm that can be used to develop diagonally implicit R–K methods

We consider an inverse problem arising from a semidefinite quadratic programming (SDQP) problem, which is a minimization problem involving l1 vector norm with positive semidefinite cone constraint. By using convex optimization theory, the first order optimality condition of the problem can be formulated as a semismooth equation. Under two assumptions, we prove that any element of the generalized Jacobian

An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a two-stage process in which the approximate solution is computed by existing numerical libraries and is then verified in a moderate computational time. The procedure

A number of stochastic mortality models with transitory jump effects have been proposed for the securitization of catastrophic mortality risks. Most of the studies on catastrophic mortality risk modeling assumed that the mortality jumps occur once a year or used a Poisson process for their jump frequencies. Although the timing and the frequency of catastrophic events are unknown, the history of the

In this paper, we develop a new deflation technique for refining or verifying the isolated singular zeros of polynomial systems. Starting from a polynomial system with an isolated singular zero, by computing the derivatives of the input polynomials directly or the linear combinations of the related polynomials, we construct a new system, which can be used to refine or verify the isolated singular zero

In this paper, inference for a multicomponent stress–strength (MSS) model is studied under censored data. When both latent strength and stress random variables follow Kumaraswamy distributions with common shape parameters, the maximum likelihood estimate of MSS reliability is established and associated approximate confidence interval is constructed using the asymptotic distribution theory and delta

This paper is concerned with the stability of a discrete kinetic approximation with a boundary scheme introduced by the authors in a previous work. We prove the weighted L2-stability of the approximation by using an identity on three-point difference schemes for convection equations. With the weighted L2-stability, the convergence of the discrete kinetic approximation can be directly established. Moreover

A uniform Haar wavelet collocation based method is proposed for finding the numerical results for a class of third order nonlinear (Emden–Fowler type) singular differential equations with initial and boundary conditions. At the point of singularity, the coefficient of the such equation blows up, that causes difficulties in capturing the numerical solutions near the point of singularity. Haar wavelet

In this study, we examined the well-known Autoregressive time series model in which innovations follow the flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The mentioned class of distributions is a rich class of distributions family that covers the robust symmetric/asymmetric light/heavy tailed distributions. A key feature of this study is using a new

Solving a linear partial differential equation witness a noteworthy role of Wright function. Due to its usefulness and various applications, a variety of its extensions (and generalizations) have been investigated and presented. The purpose and design of the paper are intended to study and come up with a new extension of the generalized Wright function by using generalized beta function and obtain

This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including

In this paper, in order to find more solutions to a nonvariational quasilinear PDE, a new augmented singular transform (AST) is developed to form a barrier surrounding previously found solutions so that an algorithm search from outside cannot pass the barrier and penetrate into the inside to reach a previously found solution. Thus a solution found by the algorithm must be new. Mathematical justifications

Two new algorithms are proposed in this paper for solving an equilibrium problem whose associated bifunction is monotone and satisfies a Lipschitz-type condition in a Hilbert space. In the first algorithm, it is assumed that the value of the Lipschitz constant of the bifunction is known while in the second one the prior knowledge of this constant is not explicitly requested. The proposed algorithms

This paper is concerned with the stability and error estimates of the local discontinuous Galerkin (LDG) method coupled with semi-implicit spectral deferred correction (SDC) time-marching up to third order accuracy for the Allen–Cahn equation. Since the SDC method is based on the first order convex splitting scheme, the implicit treatment of the nonlinear item results in a nonlinear system of equations

In this paper, we construct a new class of predictor–corrector time-stepping schemes for the Cahn–Hilliard equation, which are linear, second-order accurate in time, unconditionally energy stable, and uniquely solvable. Then, we present the stability and error estimates of the semi-discrete numerical schemes for solving the Cahn–Hilliard equation with general nonlinear bulk potentials. The semi-discrete

In this paper, a novel finite element method for solving a modified Cahn–Hilliard–Hele–Shaw system is proposed. The time discretization is based on the convex splitting of the energy functional in the modified Cahn–Hilliard equation, i.e., the high-order nonlinear term and the linear term in the chemical potential are treated explicitly and implicitly, respectively. Designing in this way leads to solving

Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated as different (strong vs. weak) formulations and are analyzed using different techniques (Fourier analysis or Green’s functions vs. functional analysis), except for

In this paper, we numerically simulate the flow of blood in two benchmark problems: the flow in a sudden expansion channel and the flow through an idealized curved coronary artery with pulsatile inlet velocity. Blood is modeled as a suspension (a non-linear complex fluid) and the movement of the red blood cell (RBCs) is modeled by using a concentration flux equation. The viscosity of blood is obtained

In the paper we study boundary-value and spectral problems for the Laplacian operator in a domain with a smooth boundary. It is assumed that on a small part of the boundary there is a Dirichlet boundary condition and on all the rest boundary there is a Steklov condition. We study the behaviour of the initial problem when a small parameter defining the size of the Dirichlet parts of the boundary tends

Using the random effects technique, this paper examines the impact of bank-specific factors on the volume of bank deposits in Ghana for the period 2008 to 2017. Controlling for macroeconomic factors, the results show that profitability, bank size, and liquidity are significant determinants of bank deposit. Macroeconomic instability proxied by inflation also exerts a negative significant impact on bank

In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints. We call this problem SIPLOG, where SIP stands for Semi-Infinite Program and LOG comes from LOG-det function. The main purpose of the paper is to develop an algorithm for efficiently

Radon–Nikodym (RN) derivative between two measures arises naturally in the affine structure of the space of probability measures with densities. Entropy, free energy, relative entropy, and entropy production as mathematical concepts associated with RN derivatives are introduced. We identify a simple equation that connects two measures with densities as a possible mathematical basis of the entropy balance

We analyze an equilibrium problem for 2D elastic body with a T-shape thin inclusion in a presence of damage. A part of the inclusion is elastic, and the other part is a rigid one. A delamination of the inclusion from the elastic body is assumed, thus forming a crack between the elastic body and the inclusion. Nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration

The first half of this work develops and analyzes the Shortley-Weller scheme (or Ghost-Fluid method with quadratic extrapolation) for a two-point boundary value problem with variable coefficients, where the boundary points are not on the uniform mesh. We prove that the local truncation error is first order convergent near the boundary, but the solution is third order accurate near the boundary and

In this paper, an energy stable, second-order mixed finite element scheme is proposed and analyzed for the thin film epitaxial growth model with slope selection. We employ second-order backward differentiation formula (BDF) scheme with a second-order stabilized term, which guarantees the long time energy stability to approximate the continuous model. In terms of the convergence analysis, the key difficulty

The authors found some errors in their above titled paper which should be corrected in this Corrigendum.

This study proposes a parametric implicit large eddy simulation (LES) strategy for the simulation of incompressible turbulence given by the Taylor–Green vortex. Our proposed scheme is derived from the dispersion-relation-preserving (DRP) philosophy to provide a specified numerical dissipation through a free modeling parameter. The specification of this dissipation control parameter represents a unique

Mixed Volterra-Fredholm integral equations can arise from mathematical modelling of the spatio-temporal development of an epidemic. In this paper a hybrid Legendre block-pulse method is used to provide solutions to a general integral equation of this type. The main idea of this approach is to reduce a Volterra-Fredholm integral equation to a system of algebraic equations. An order convergence analysis

In this paper, our main goal is to study the convergence analysis of adaptive edge finite element method (AEFEM) based on arbitrary order Nédélec edge elements for the variable-coefficient time-harmonic Maxwell’s equations, i.e., we prove that the AEFEM gives a contraction for the sum of the energy error and the error estimator, between two consecutive adaptive loops provided the initial mesh is fine

We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and spectral content of these sources are developed and numerically tested using Finite Element Mesh simulations. The resulting framework for heat source reconstruction