Related papers: Divergence preservation in the ADI algorithms for …
For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 um the…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
We derive thermodynamically consistent models for diblock copolymer solutions coupled with the electric and magnetic field, respectively. These models satisfy the second law of thermodynamics and therefore are therefore thermodynamically…
We consider the thermodynamic consistency of the charge response function in the (extended) Hubbard model. In DMFT, thermodynamic consistency is preserved. We prove that the static, homogeneous DMFT susceptibility is consistent as long as…
The $\phi$-divergence-based moment method was recently introduced Abdelmalik et al. (2023) for the discretization of the radiative transfer equation. At the continuous level, this method is very close to the entropy-based MN methods and…
The dispersion error is often the dominant error for computed solutions of wave propagation problems with high-frequency components. In this paper, we define and give explicit examples of $\alpha$-dispersion-relation-preserving schemes.…
Moving grids are of interest in the numerical solution of hydrodynamical problems and in numerical relativity. We show that conventional integration methods for the simple wave equation in one and more than one dimension exhibit a number of…
In this paper the unconditional stability of four well-known ADI schemes is analyzed in the application to time-dependent multidimensional diffusion equations with mixed derivative terms. Necessary and sufficient conditions on the parameter…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
In this work, we study two-dimensional diffusion-wave equations with variable exponent, modeling mechanical diffusive wave propagation in viscoelastic media with spatially varying properties. We first transform the diffusion-wave model into…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
Investigation of the approximation properties, convergence, and stability of the ADER-DG method for solving an ODE system is carried out. The ADER-DG method is $A$- and $AN$-stable, $L$-stable, $B$- and $BN$-stable, and algebraically…
In this work we present a structure preserving discretization for turbidity currents based on a mass-, energy-, enstrophy-, and vorticity-conserving formulation for 2D incompressible flows. This discretization exploits a dual-field…
This paper is concerned with the optimal error estimates and energy conservation properties of the alternating direction implicit finite-difference time-domain (ADI-FDTD) method which is a popular scheme for solving the 3D Maxwell…
We study the non relativistic motions of a charged particle in the electromagnetic field generated by two parallel electrically neutral vertical wires carrying time depends currents. Under quantitative conditions on the currents we prove…
Permanent electric dipole moments (EDMs) violate parity and time reversal symmetry. Within the Standard Model (SM) they are many orders of magnitude below present experimental sensitivity. Many extensions of the SM predict much larger EDMs,…
In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…