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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An inverse Lax-Wendroff procedure for finite difference schemes on the Cartesian grids
笛卡尔网格 有限差分格式 Lax-Wendroff逆过程
2023/11/13
In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Number of rational points of difference varieties in finite difference fields
有限差分域 差分簇 有理点数
2023/4/13
A difference field is a field with a distinguished automorphism. Automorphisms of a finite field are powers of the Frobenius map. In this talk, I will discuss how to estimate the number of rational po...
A sweeping preconditioner for Yee’s finite difference approximation of time-harmonic Maxwell’s equations
Electromagnetic scattering Yee grid finite difference methods perfectly matched layers LDLT factorizations multifrontal method wave propagation in inhomogeneous and anisotropic media matrix preconditioners
2015/7/14
This paper is concerned with the fast iterative solution of linear systems arising from finite difference discretizations in electromagnetics. The sweeping preconditioner with moving perfectly matched...
The Best Finite-Difference Scheme for the Helmholtz Equation
The Best Finite-Difference Scheme for the Helmholtz and Laplace’s Equations
2013/1/30
The best finite-difference scheme for the Helmholtz equation is suggested. A method of solving obtained finite-difference scheme is developed. The efficiency and accuracy of method were tested on seve...
Elements of Polya-Schur theory in finite difference setting
Elements Polya-Schur theory finite difference setting Classical Analysis and ODEs
2012/4/16
In this note we attempt to develop an analog of P\'olya-Schur theory describing the class of univariate hyperbolicity preservers in the setting of linear finite difference operators. We study the clas...
Uniform convergence analysis of an upwind finite difference approximations of an homogenous singularly perturbed boundary value problem using grid equidistribution
singular perturbation adaptive grid rate of convergence error estimate
2011/10/13
We derive varepsilon-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here,...
Consistency Analysis of Finite Difference Approximations to PDE Systems
systems of partial differential equations involution Thomas decomposition finite difference approximations consistency
2011/9/16
Abstract: In the given paper we consider finite difference approximations to systems of polynomially-nonlinear partial differential equations whose coefficients are rational functions over rationals i...
Finite difference approximations for the first-order hyperbolic partial differential equation with point-wise delay
hyperbolic partial differential equation differential difference equation
2011/1/18
Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equa...
Finite-difference analysis for unsteady squeezing flow of a second grade fluid between circular plates
Non-Newtonian fluids Squeezing flow
2010/9/27
The unsteady two-dimensional flow of non-conducting, incompressible second grade fluid between two circular plates approaching or receding from each other symmetrically is studied. A similarity transf...
Numerical solution to Belousov朲habotinskii model and a comparison with the finite difference method
Traveling wavelets method reaction- diffusion system
2010/9/10
In this work, we find a numerical solution to Belousov – Zhabontinskii system, we use the traveling wavelets method. It is well known that this model describes a chemical reaction. The results obtaine...
An explicit finite difference scheme for a compressible Heisenberg chain equations
compressible Heisenberg chain equations explicitness
2010/9/14
In this paper, we consider a class of compressible Heisenberg chain equations with periodic initial value problem. An explicit finite difference scheme is proposed. Moreover, its convergence and stabi...
Solving one-dimensional advection-dispersion with reaction using some finite-difference methods
Advection Dispersion Finite-difference
2010/9/14
In this paper we have solved the one-dimensional advection-dispersion equation with reaction using some finite-difference methods, namely, FTCS used by B.Ataie-Ashtiani et al. (1996), (we call it FTCS...
A Finite Difference Method for Studying Thermal Deformation in 3D Double-Layered Micro- Structures Exposed to Ultrashort-Pulsed Lasers
Finite Difference Thermal Deformation Ultrashort-Pulsed Lasers
2008/11/10
Ultrashort-pulsed lasers have been attracting worldwide interest in science and engineering. Studying the thermal deformation induced by ultrashort-pulsed lasers is important for preventing thermal da...
On Multidimensional Ostrowski and Grüss Type Finite Difference Inequalities
Multidimensional Ostrowski and Grüss type inequalities Finite difference inequalities Forward differences Empty sum Identities
2008/6/30
The aim of this paper is to establish some new multidimensional finite difference inequalities of the Ostrowski and Grüss type using a fairly elementary analysis.
Error analysis for weighted higher order compact finite difference scheme
Finite Difference Schemes High Order Compact Schemes
2010/9/16
In this paper, we analyze a type of finite-difference schemes, a newly developed Weighted Compact Scheme (WCS) developed by L. Jiang L, H.Shan, C. Liu, [Weight Compact Scheme for Shock Capturing, Inte...