TY  - JOUR
TI  - Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)
AB  - In this paper, we consider the Burgers equation B(2, 2) . Exact and nonstandard finite difference schemes(NSFD) for the Burgers equation B(2, 2) are designed. First, two exact finite difference schemes for the Burgers equationB(2, 2) are proposed using traveling wave solution. Then, two NSFD schemes are represented for this equation. Thesetwo NSFD schemes are compared with a standard finite difference (SFD) scheme. Numerical results show that the NSFDschemes are accurate and efficient in the numerical simulation of the kink-wave solution of the B(2, 2) equation. We seethat although the SFD scheme yields numerical instability for large step sizes, NSFD schemes provide reliable results forlong time integration. Local truncation errors show that the NSFD schemes are consistent with the B(2, 2) equation.
AU  - AYDIN, Ayhan
AU  - KÖROĞLU, CANAN
DO  - 10.3906/mat-2009-51
PY  - 2021
JO  - Turkish Journal of Mathematics
VL  - 45
IS  - 2
SN  - 1300-0098
SP  - 647
EP  - 660
DB  - TRDizin
UR  - http://search/yayin/detay/443228
ER  -