Home – Home – Jornals – Advanced Search

Aiming at the problem that observation errors exist in both the observation vector and the coefficient matrix for an autoregressive model, a new parameter estimation method is proposed. First, the observation vector and coefficient matrix are recombined, which avoids the situation that the same observation value appears in both the observation vector and the coefficient matrix. Then a detailed algorithm is derived based on the principle of total least squares and indirect adjustment. Finally, the effectiveness and feasibility of the proposed method are verified by an analysis of validation and simulation examples and compared with the weighted total least squares and the correlation total least squares.

This paper introduces an approach for approximating solutions to multi-high-order fractional-differential equations by employing the Caputo fractional derivative, along with initial conditions. The technique is based on standard collocation points and Touchard polynomials. The linear equation and its initial conditions can be transformed into matrix relations by the new method, making it easier to solve a linear algebraic equation with generalized Touchard coefficients as unknowns. Also, emphasizing computational efficiency, the method is illustrated with examples.

Some iterative processes in Krylov subspaces are considered for solving systems of linear algebraic equations (SLAE) with high-order sparse matrices that arise in grid approximations of multidimensional boundary value problems. The SLAE are preconditioned by a uniform combined method that includes domain decomposition and recursive application of a two-grid algorithm, which are implemented by forming block-tridiagonal algebraic and grid structures inverted by using incomplete factorization and diagonal compensation. For some Stieltjes systems, stability and convergence of iterations are studied. Parallelization and generalization of the methods to wider classes of relevant practical problems are discussed.

Algorithms for solving ensembles of ODEs with sets of different input data arising from modeling chemical kinetics are considered with an operator splitting scheme for multiphysical calculations. The efficiency of an algorithm combining clustering of an input data ensemble and estimating of the solution within the cluster is evaluated by using a sensitivity matrix obtained by solving adjoint equations. The algorithm is implemented on the basis of numerical schemes consistent in the sense of a discrete Lagrange identity for solving ODE systems of the production-destruction type. The contribution of the clustering and the sensitivity matrix to the performance of the algorithm is evaluated. The results of testing the algorithm with atmospheric chemistry scenarios show that the algorithm allows one to reduce the calculation time with an acceptable decrease in accuracy.

We study a one-dimensional problem of an infinite tube which is open in the right and there is a piston put at one end in the left. Due to the fact that the computational domain is finite while the domain of the problem is infinite, the numerical result is affected by the presence of a reflected wave that appears when a shock travels to the right and interacts with the right boundary. Thus there is a need of implementing a non-reflecting boundary condition in order to eliminate as much as possible the effect of the reflected wave. In this paper, we use the Euler equations in mass Lagrangian coordinates as the governing equations and apply a finite volume method to compute the numerical solution. In order to deal with the reflected wave, we use a Burgers-like equation in an additional computational domain. The numerical results we obtain show that the numerical error is reduced significantly.

This paper presents a two-grid method for solving nonlinear time fractional diffusion equations (TFDEs). First, a fully discrete scheme is constructed by using P²₀- P₁ mixed finite elements (MFEs) and L1 formula for spatial and temporal discretization, respectively. Second, the stability and error of the fully discrete scheme are analyzed. Third, a two-grid algorithm (TGA) based on the fully discrete scheme is proposed and its stability and error analysis results are derived. Finally, some numerical examples are provided to support the theoretical results.

We consider the ill-posed problem of localizing (finding the position of) the discontinuity lines of a function of two variables, provided that outside the discontinuity lines the function satisfies a Lipschitz condition, and at each point on the lines there is a discontinuity of the first kind. For a uniform grid with step τ, it is assumed that at each node the mean values of the perturbed function on a square with side τ are known, and the perturbed function approximates the exact function in L₂(ℝ²). The level of perturbation δ is assumed to be known. We propose a new approach to construct regularizing algorithms for localizing the discontinuity lines based on a separation of the original noisy data. New algorithms are constructed for a class of functions with piecewise linear discontinuity lines and a convergence theorem with estimates of approximation accuracy is proved.

A morphing algorithm included in a three-dimensional structured grid generation technology designed for the numerical solution of differential equations modeling vortex processes in multi-component hydrodynamics is described. The algorithm is intended for the generation of structured grids of a special topology in volumes obtained by deformation of volumes of revolution by the bodies formed by surfaces of revolution with parallel axes. The algorithm is developed by using a variational approach for constructing optimal grids and is a non-stationary one: at each iteration the form of a domain and the grid for it are deformed. Then the grid is optimized in accordance with the following optimality criterion: the closeness of the grid to a uniform and orthogonal one. The iterations are continued up to a given degree of deformation. The algorithm allows one to construct grids in domains of very complex geometry, and it is not necessary to describe the boundary of a complex domain, it is sufficient to describe the volume of revolution, the deforming volume, and the parameters of deformation. Examples of grid calculations are given.

During dynamic loading, ice demonstrates complex nonlinear behavior, which depends on many factors, including strain rate. In practical applications, low-speed collision processes occur, in which ice exhibits both viscous and brittle properties. To consider the specifics of local ice failure, a compound model is proposed in this paper, which distinguishes a hydrostatic core and an elastoplastic zone in ice, with the material far from the impact area in the elastic state. Additionally, volumetric cracking is considered. The model is verified by comparing the results of numerical computations and a laboratory experiment with a spherical indenter. The numerical results demonstrate various phenomena observed in the experiments. The simulations reconstruct nonlinear waves, different destruction patterns, and show the wave nature of fracturing. The deformation curves calculated confirm the possibility of a qualitative description of ice behavior during the main stage of the collision.

It is well known that if diagonalizable matrices A and B commute, then they can be brought to diagonal form via one and the same similarity transformation. We prove an analog of this statement related to nonsingular unitoid matrices and Hermitian congruence transformations. A matrix is said to be unitoid if it can be brought to diagonal form via a congruence transformation.