scholarly journals Two Conservative Difference Schemes for Rosenau-Kawahara Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Jinsong Hu ◽  
Youcai Xu ◽  
Bing Hu ◽  
Xiaoping Xie
Keyword(s):  
Finite Difference ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Kawahara Equation ◽  
Conservative Difference Schemes ◽  
The Difference ◽  
Second Order Convergence ◽  
Initialboundary Value Problem ◽  
Conservative Difference ◽  
Theoretical Results

Two conservative finite difference schemes for the numerical solution of the initialboundary value problem of Rosenau-Kawahara equation are proposed. The difference schemes simulate two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference schemes are of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

scholarly journals On the difference method for approximation of second order derivatives of a solution of Laplace’s equation in a rectangular parallelepiped

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 633-643
Author(s):  
Adiguzel Dosiyev ◽  
Hediye Sarikaya
Keyword(s):  
Difference Schemes ◽  
Rectangular Parallelepiped ◽  
Finite Difference Schemes ◽  
Compatibility Conditions ◽  
Averaging Operator ◽  
Second Derivatives ◽  
Boundary Functions ◽  
The Difference ◽  
Derivatives Of ◽  
Theoretical Results

We present and justify finite difference schemes with the 14-point averaging operator for the second derivatives of the solution of the Dirichlet problem for Laplace?s equations on a rectangular parallelepiped. The boundary functions ?j on the faces ?j,j = 1,2,..., 6 of the parallelepiped are supposed to have fifth derivatives belonging to the H?lder classes C5?, 0 < ? < 1. On the edges, the boundary functions as a whole are continuous, and their second and fourth order derivatives satisfy the compatibility conditions which result from the Laplace equation. It is proved that the proposed difference schemes for the approximation of the pure and mixed second derivatives converge uniformly with order O(h3+?), 0 < ? < 1 and O(h3), respectively. Numerical experiments are illustrated to support the theoretical results.

scholarly journals Conservative Linear Difference Scheme for Rosenau-KdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinsong Hu ◽  
Youcai Xu ◽  
Bing Hu
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Kdv Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
The Difference ◽  
Second Order Convergence ◽  
Initial Boundary Value ◽  
Theoretical Results

A conservative three-level linear finite difference scheme for the numerical solution of the initial-boundary value problem of Rosenau-KdV equation is proposed. The difference scheme simulates two conservative quantities of the problem well. The existence and uniqueness of the difference solution are proved. It is shown that the finite difference scheme is of second-order convergence and unconditionally stable. Numerical experiments verify the theoretical results.

FINITE DIFFERENCE SCHEMES FOR A CERTAIN NONLINEAR PARABOLIC SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 679-699
Author(s):  
HOMARE MORIOKA ◽  
ATUSI TANI
Keyword(s):  
Weak Solution ◽  
Finite Difference ◽  
Artificial Viscosity ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Nonlinear Parabolic System ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Nonlinear Parabolic ◽  
The Difference

This paper is devoted to study the global existence of a solution of bounded variation to the initial value problem for a system of conservation laws with artificial viscosity. The method of finite difference schemes of implicit type is used. We prove that the difference approximations converge to a weak solution of the problem. Moreover, this weak solution is really a classical solution according to the Oleĭnik's argument.

Finite Difference Schemes for Poro-elastic ProblemS

2002 ◽  
Vol 2 (2) ◽  
pp. 132-142 ◽  
Author(s):  
Francisco J. Gaspar ◽  
Francisco J. Lisbona ◽  
Petr N. Vabishchevich
Keyword(s):  
Finite Difference ◽  
A Priori Estimates ◽  
Classical Model ◽  
A Priori ◽  
Fluid Pressure ◽  
Rectangular Domain ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
The Matrix ◽  
The Difference

AbstractIn this paper, we present a finite difference analysis of the consolidation problem for saturated porous media. In the classical model, the behaviour of the porous environment – fluid system is described by a set of equations for the unknown vector displacements of the matrix skeleton and the fluid pressure. For simplicity we consider a model problem with constant coefficients in a rectangular domain. A priori estimates for the difference solution of the problem are obtained and on their basis the convergence of two-level difference schemes is investigated.

scholarly journals Conservative Difference Scheme for Generalized Rosenau-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yan Luo ◽  
Youcai Xu ◽  
Minfu Feng
Keyword(s):  
Difference Scheme ◽  
Kdv Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Discrete Analogue ◽  
The Difference ◽  
Second Order Convergence ◽  
Initial Boundary Value ◽  
Conservative Difference ◽  
Theoretical Results

A conservative Crank-Nicolson finite difference scheme for the initial-boundary value problem of generalized Rosenau-KdV equation is proposed. The difference scheme shows a discrete analogue of the main conservation law associated to the equation. On the other hand the scheme is implicit and stable with second order convergence. Numerical experiments verify the theoretical results.

scholarly journals STATIONARY PROBLEMS WITH NONLOCAL BOUNDARY CONDITIONS

2001 ◽  
Vol 6 (2) ◽  
pp. 178-191 ◽  
Author(s):  
R. Čiegis ◽  
A. Štikonas ◽  
O. Štikoniene ◽  
O. Suboč
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Difference Schemes ◽  
Maximum Norm ◽  
Finite Difference Schemes ◽  
Stability Estimates ◽  
Stationary Problems ◽  
Theoretical Results

In this article a stationary problems with general nonlocal boundary conditions is considered. The differential problems and finite difference schemes for solving this problem are investigated. Stability estimates are proved in the maximum norm and the non‐negativity of the solution is investigated. All theoretical results are illustrated by representative examples.

scholarly journals Conservative finite difference schemes for the modified Camassa-Holm equation

JSIAM Letters ◽  
2011 ◽  
Vol 3 (0) ◽  
pp. 37-40 ◽  
Author(s):  
Yuto Miyatake ◽  
Takayasu Matsuo ◽  
Daisuke Furihata
Keyword(s):  
Finite Difference ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Holm Equation
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