Related papers: Comparison of estimates for dispersive equations
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
In [7], a new iterative method for solving linear system of equations was presented which can be considered as a modification of the Gauss-Seidel method. Then in [4] a different approach, say 2D-DSPM, and more effective one was introduced.…
The spherical cap discrepancy is a widely used measure for how uniformly a sample of points on the sphere is distributed. Being hard to compute, this discrepancy measure is typically replaced by some lower or upper estimates when designing…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
This article is devoted to the analysis of the convergence rates of several nu- merical approximation schemes for linear and nonlinear Schr\"odinger equations on the real line. Recently, the authors have introduced viscous and two-grid…
We study oscillatory integrals of the type ${\mathcal F}^{-1}(e^{ita(\cdot)}\psi(\cdot))$ where $a$ is a general function satisfying some elliptic type and non-degenerate conditions at both the origin and infinity, and $\psi$ belongs to…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
Variational approaches to disparity estimation typically use a linearised brightness constancy constraint, which only applies in smooth regions and over small distances. Accordingly, current variational approaches rely on a schedule to…
To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
In this paper, we introduce a class of stochastic partial differential equations (SPDEs) with fractional time-derivatives, and study the $L_2$-theory of the equations. This class of SPDEs can be used to describe random effects on transport…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.
The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…