相关论文: Exponential-sum-approximation technique for variab…
This paper deals with the asymptotic behavior and FEM error analysis of a class of strongly damped wave equations using a semidiscrete finite element method in spatial directions combined with a finite difference scheme in the time…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
A semidiscrete Galerkin finite element method applied to time-fractional diffusion equations with time-space dependent diffusivity on bounded convex spatial domains will be studied. The main focus is on achieving optimal error results with…
In this paper, a semi-discrete spatial finite volume (FV) method is proposed and analyzed for approximating solutions of anomalous subdiffusion equations involving a temporal fractional derivative of order $\alpha \in (0,1)$ in a…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
In the paper, we present a high order fast algorithm with almost optimum memory for the Caputo fractional derivative, which can be expressed as a convolution of $u'(t)$ with the kernel $(t_n-t)^{-\alpha}$. In the fast algorithm, the…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
Searches for impulsive, astrophysical transients are often highly computationally demanding. A notable example is the dedispersion process required for performing blind searches for Fast Radio Bursts (FRBs) in radio telescope data. We…
In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
The well-known Caputo fractional derivative and the corresponding Caputo fractional integral occur naturally in many equations that model physical phenomena under inhomogeneous media. The relationship between the two fractional terms can be…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…
It has been well documented that the use of exponentially-averaged momentum (EM) in particle swarm optimization (PSO) is advantageous over the vanilla PSO algorithm. In the single-objective setting, it leads to faster convergence and…
In this paper, we introduce a new scheme for the efficient numerical treatment of the electronic Schr\"odinger equation for molecules. It is based on the combination of a many-body expansion, which corresponds to the so-called bond order…
In this paper, we consider the numerical approximation of time-fractional parabolic problems involving Caputo derivatives in time of order $\alpha$, $0< \alpha<1$. We derive optimal error estimates for semidiscrete Galerkin FE type…
Stellarator boundary optimization faces a fundamental numerical challenge: the extreme disparity between low- and high-mode amplitudes creates an optimization landscape in which direct full-spectrum approaches typically converge to poor…
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…