scholarly journals Convergence of a fully discrete finite difference scheme for the Korteweg–de Vries equation

2014 ◽  
Vol 35 (3) ◽  
pp. 1047-1077 ◽  
Author(s):  
Helge Holden ◽  
Ujjwal Koley ◽  
Nils Henrik Risebro
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Vries Equation ◽  
Fully Discrete ◽  
De Vries

scholarly journals An Unconventional Finite Difference Scheme for Modified Korteweg-de Vries Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Canan Koroglu ◽  
Ayhan Aydin
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Truncation Error ◽  
Vries Equation ◽  
Mkdv Equation ◽  
Numerical Results ◽  
De Vries ◽  
Nsfd Scheme ◽  
Theta Method

A numerical solution of the modified Korteweg-de Vries (MKdV) equation is presented by using a nonstandard finite difference (NSFD) scheme with theta method which includes the implicit Euler and a Crank-Nicolson type discretization. Local truncation error of the NSFD scheme and linear stability analysis are discussed. To test the accuracy and efficiency of the method, some numerical examples are given. The numerical results of NSFD scheme are compared with the exact solution and a standard finite difference scheme. The numerical results illustrate that the NSFD scheme is a robust numerical tool for the numerical integration of the MKdV equation.

scholarly journals INVESTIGATION OF A COST‐EFFECTIVE FINITE DIFFERENCE SCHEME FOR THE TRANSPORT EQUATION

2003 ◽  
Vol 8 (3) ◽  
pp. 247-258
Author(s):  
D. G. Slugin ◽  
A. V. Popov
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Transport Equation ◽  
Finite Difference Scheme ◽  
Three Dimensional ◽  
Cost Effective ◽  
Differential Approximation ◽  
Fully Discrete ◽  
Implicit Finite Difference Scheme ◽  
Implicit Finite Difference

The transport equation for three‐dimensional flow of a viscous gas is considered. An implicit finite difference scheme is constructed for approximating the transport equation. The error estimation is proved. The main part of the analysis is done for the first differential approximation of the proposed finite difference scheme, but the results are also valid in the fully discrete case.

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