Related papers: Stable finite difference methods for Kirchhoff-Lov…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
The aim of this paper is to develop fast second-order accurate difference schemes for solving one- and two-dimensional time distributed-order and Riesz space fractional diffusion equations. We adopt the same measures for one- and…
We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved…
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We present an approach to simulate the 3D isotropic elastic wave propagation using nonuniform finite difference discretization on staggered grids. Specifically, we consider simulation domains composed of layers of uniform grids with…
For love dynamical models, a new idea combining piecewise concept for integer-order, stochastic, and fractional derivatives is presented in order to capture the chaos and several crossover emotional scenerios. Under the assumptions of…
In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…
We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem)…
We develop a stable and efficient numerical scheme for modeling the optical field evolution in a nonlinear dispersive cavity with counter propagating waves and complex, semiconductor physics gain dynamics that are expensive to evaluate. Our…
In this work we develop a novel fully discrete version of the plates complex, an exact Hilbert complex relevant for the mixed formulation of fourth-order problems. The derivation of the discrete complex follows the discrete de Rham…
This paper presents a reliable and efficient residual-based a posteriori error analysis for the symmetric $H(\operatorname{div}\operatorname{div})$ mixed finite element method for the Kirchhoff-Love plate bending problem with mixed boundary…
A crucial part of successful wave propagation related inverse problems is an efficient and accurate numerical scheme for solving the seismic wave equations. In particular, the numerical solution to a multi-dimensional Helmholtz equation can…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with…
Based on the weighted and shifted Gr\"{u}nwald difference (WSGD) operators [24], we further construct the compact finite difference discretizations for the fractional operators. Then the discretization schemes are used to approximate the…
Finite difference approximation, in addition to Taylor truncation errors, introduces numerical dispersion-and-dissipation errors into numerical solutions of partial differential equations. We analyze a class of finite difference schemes…