Related papers: Removing numerical dispersion from linear evolutio…
A finite difference algorithm based on the integral Laguerre transform in time for solving a three-dimensional one-way wave equation is proposed. This allows achieving high accuracy of calculation results. In contrast to the Fourier method,…
The main purpose of this paper is to improve our transposition method to solve both vector-valued and operator-valued backward stochastic evolution equations with a general filtration. As its application, we obtain a general Pontryagin-type…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
The study of strongly out-of-equilibrium states and their time evolution towards thermalization is critical to the understanding of an ever widening range of physical processes. We present a numerical method that for the first time allows…
In this overview paper, we show existence of smooth solitary-wave solutions to the nonlinear, dispersive evolution equations of the form \begin{equation*} \partial_t u + \partial_x(\Lambda^s u + u\Lambda^r u^2) = 0, \end{equation*} where…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…
The finite-difference time-domain (FDTD) method is a well established method for solving the time evolution of Maxwell's equations. Unfortunately the scheme introduces numerical dispersion and therefore phase and group velocities which…
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
In this paper we consider a sub-diffusion problem where the fractional time derivative is approximated either by the L1 scheme or by Convolution Quadrature. We propose new interpretations of the numerical schemes which lead to a posteriori…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are…
In this paper we introduce an evolutionary algorithm for the solution of linear integer programs. The strategy is based on the separation of the variables into the integer subset and the continuous subset; the integer variables are fixed by…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
Evolutionary synthesis models are a fundamental tool to interpret the properties of observed stellar systems. In order to achieve a meaningful comparison between models and real data, it is necessary to calibrate the models themselves, i.e.…
In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate…
We analyze a homogenization limit for the linear wave equation of second order. The spatial operator is assumed to be of divergence form with an oscillatory coefficient matrix $a^\varepsilon$ that is periodic with characteristic length…