This study introduces a multiscale simulation approach, employing the Meshfree Generalized Multiscale Finite Element Method (GMsFEM), to numerically model fluid seepage in permafrost soil conditions. Combining Meshfree and Finite Element Methods, the coarse-grid system is addressed, while the standard Finite Element Method operates on the fine grid. For representing fractures at the fine grid level, the Discrete Fracture Model (DFM) is utilized. The findings demonstrate the method’s efficacy in accurately depicting soil heterogeneity and the impact of fractures on soil temperature.

System identification determines the model of the plant from the measurement data and has been widely used in the prediction and control. In this paper, the parameter estimation problem is studied for multivariate equation-error systems with autoregressive moving average noises. Since the considered system is high-dimensional, the distributed identification is considered in this paper. The subsystems are obtained by decomposing the original system in accordance with the number of the outputs. However, the subsystems contain the same parameter vector, resulting in many redundant estimates. By taking the average of the parameter estimation vectors, we develop a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm to cut down the redundant parameter estimates. In consideration of the information communication between the subsystems and the convergence of the estimation algorithm, a partially-coupled RGELS (PC-RGELS) algorithm is presented by means of the coupling identification concept. Compared with the multivariate RGELS algorithm, the two algorithms have higher computational efficiencies. Finally, an illustrative example is provided to demonstrate the effectiveness of the two proposed algorithms.

In this paper, the constrained nonconforming rotated Q1 (CNQ1rot) element is employed to study the superconvergence behavior of the backward-Euler (B-E) and Crank–Nicolson (C–N) fully-discrete schemes for the parabolic equation. By applying the mean-value and integral identities techniques, a novel high-accuracy estimate for the CNQ1rot element is proved on anisotropic meshes rigorously, which is essential to derive the superclose result. Then, the superconvergence results for the above two schemes are deduced with the help of the interpolation post-processing approach, respectively. Eventually, some numerical experiments are carried out to verify the rationality of the theoretical analysis.

This paper is concerned with the numerical solutions of Schrödinger–Boussinesq (SBq) system by an orthogonal spline collocation (OSC) discretization in space and Crank–Nicolson (CN) type approximation in time. By using the mathematical induction argument and standard energy method, the proposed CN+OSC scheme is proved to be unconditionally convergent at the order O(τ2+h4) with mesh-size h and time step τ in the discrete L2-norm. We devise a new computation method based on the orthogonal diagonalization techniques (ODT) to realize the proposed CN+OSC scheme. In order to compare the performance of ODT, we devise an alternating direction implicit (ADI) method to compute the CN+OSC scheme for high spatial dimension SBq system. As an alternative implementation, the new method ODT not only exhibits more accurate numerical results, but also demonstrates stronger invariance preserving ability. Numerical results are reported to verify the error estimates and the discrete conservation laws.

In this paper, we realize a rapid, smooth iterative morphing algorithm between two immersed and closed spherical curves of arbitrary turning numbers. By compensating in turning numbers, we linearly interpolate between geodesic curvatures and the side lengths of their accurate spherical polygons approximation. Our algorithm is essentially based on a geometrical closure condition for a flow of spherical polygons involving the variation of both sides and exterior angles. A curvature smoothing flow using discrete geodesic curvature is adopted for smooth curve generation. To demonstrate the good properties of the method, a morphing of spherical curves and ruled surfaces is illustrated.

This paper introduces Jacobian-free Locally Linearized Runge–Kutta formulas of Dormand and Prince for integrating large systems of initial value problems. With these new Jacobian-free formulas, an adaptive time-stepping variable-order scheme with regulated Krylov dimension is constructed with new developments in the computation of the phi-function action over vectors through Jacobian-free Krylov–Padé approximations, and in the procedures for controlling the approximation errors and for estimating the dimension of the Krylov subspaces. At each integration step, the implemented scheme performs only one Krylov subspace decomposition and a few computations of low dimensional exponential matrices, which contrasts with the implementation of other exponential-type integrators of high order. Regarding to existing schemes, the performed numerical study demonstrates a higher effectiveness of the constructed scheme in the integration of a variety of test equations.

The paper introduces novel parametric estimators for the mean value function (MVF) and variance function (VF) in geometric processes (GPs) based on a random sample which belongs to a GP. Specifically, it addresses scenarios where the distribution function of the first interarrival time of GP is analytically known, but its parameters, along with the ratio parameter of the GP, are unknown. It establishes a solid theoretical foundation for the estimators proposed and investigates some statistical properties such as strong consistency and asymptotic unbiasedness of the estimators. These results generalize some of the findings acquired in previous studies. To evaluate the performance of the proposed estimators, we conduct a comprehensive Monte Carlo simulation study. This involves using various lifetime distributions, such as gamma, Weibull, and lognormal considering different sample sizes and parameter values. A discussion of an application to software engineering is also provided to illustrate the applicability of the methods developed in this study.

In this paper, collocation methods for linear Volterra integral equations with highly oscillatory trigonometric kernels are considered. Different from the cases with linear oscillator, we need a further action to obtain a practical scheme for general oscillators. To deal with it, the moment free Filon type method is employed in the exact collocation equation resulting to a fully discretized one. In order to conduct the convergence analysis, we firstly study the highly oscillatory integrals occurring in the error equations. Both the theoretical and numerical results show that our method not only converges with respect to step length but also has an asymptotic order which could be two. The asymptotic order indicates that the numerical results will become more accurate as the increase of frequency.

In this work, we study the Hermite interpolation on n-dimensional non-equally spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. Initially, we prove the uniqueness of the interpolating polynomial, followed by deriving a concise closed expression that employs a solitary summation, independent of dimensionality, which is algebraically simpler than the only alternative closed form for the n-dimensional classical Hermite interpolation (Gasca and Sauer, 2000). We also provide the remainder of the interpolation in integral form; we derive the ideal of the interpolation and express the interpolation remainder using only polynomial divisions, in the case of interpolating a polynomial function. Moreover, we prove the continuity of Hermite polynomials defined on adjacent n-dimensional grids, thus establishing spline behavior. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, in the simple case of few points, as well as hundreds of points on 3D-grids using a spline-like interpolation, which compares favorably to state-of-the-art spline interpolation methods.

The classical compound Poisson risk model and the Sparre-Andersen risk model for insurance businesses assume that the interclaim times and the claim amounts are independently distributed. To relax the independence assumption, we consider a continuous-time risk model under which the interclaim-time distribution depends on the size of the previously occurred claim. For practical purposes, the surplus process is further assumed to be perturbed by a Brownian motion to address small financial fluctuations or investment returns. To analyze the risk associated with the event when the insurer’s ruin occurs, explicit solutions for the Gerber–Shiu discounted penalty function may be derived through the defective renewal equations provided here when claim amounts follow an arbitrary distribution. Applications with Kn family claim amounts and the Laplace transform of the ruin time are discussed in detail. An illustrative numerical example is presented to assess the impact of different perturbations on the underlying dependent-structure surplus process.