Related papers: Multiple Iterative Splitting method for Higher ord…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
Addressing large-scale indefinite least squares (ILS) problem poses notable computational bottlenecks in the field of numerical linear algebra. State-of-the-art iterative schemes for such problems are predominantly constructed upon the…
In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…
In this paper we propose a multiscale method for the acoustic wave equation in highly oscillatory media. We use a higher-order extension of the localized orthogonal decomposition method combined with a higher-order time stepping scheme and…
We are motivated to solve differential algebraic equations with new multi-stage and multisplitting methods. The multi-stage strategy of the waveform relaxation (WR) methods are given with outer and inner iterations. While the outer…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
Matrix double splitting iterations are simple in implementation while solving real non-singular (rectangular) linear systems. In this paper, we present two Alternating Double Splitting (ADS) schemes formulated by two double splittings and…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
An efficient numerical algorithm for the laser driven multi-level ionization of high-atomic-number gases is proposed and implemented in an electromagnetic particle-in-cell code SPACE. The algorithm is based on analytical solutions to the…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the $H^{-1}$-gradient flow of the…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
The splitting method is a powerful method for solving partial differential equations. Various splitting methods have been designed to separate different physics, nonlinearities, and so on. Recently, a new splitting approach has been…
The iterative problem of solving nonlinear equations is studied. A new Newton like iterative method with adjustable parameters is designed based on the dynamic system theory. In order to avoid the derivative function in the iterative…
Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an $N$-level model atom, the technique avoids the $N^{3}$ scaling in…
On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…