Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)

AYDIN, Ayhan; KÖROĞLU, CANAN

doi:10.3906/mat-2009-51

Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)

Canan KÖROĞLU, (Hacettepe Üniversitesi Fen Fakültesi Matematik Bölümü, Ankara, Türkiye)

Ayhan AYDIN (Atılım Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)

Turkish Journal of Mathematics

1 0

Yıl: 2021 Cilt: 45 Sayı: 2 Sayfa Aralığı: 647 - 660 Metin Dili: İngilizce DOI: 10.3906/mat-2009-51 İndeks Tarihi: 22-09-2021

Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)

Öz:

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.

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APA	KÖROĞLU C, AYDIN A (2021). Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). , 647 - 660. 10.3906/mat-2009-51
Chicago	KÖROĞLU CANAN,AYDIN Ayhan Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). (2021): 647 - 660. 10.3906/mat-2009-51
MLA	KÖROĞLU CANAN,AYDIN Ayhan Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). , 2021, ss.647 - 660. 10.3906/mat-2009-51
AMA	KÖROĞLU C,AYDIN A Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). . 2021; 647 - 660. 10.3906/mat-2009-51
Vancouver	KÖROĞLU C,AYDIN A Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). . 2021; 647 - 660. 10.3906/mat-2009-51
IEEE	KÖROĞLU C,AYDIN A "Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)." , ss.647 - 660, 2021. 10.3906/mat-2009-51
ISNAD	KÖROĞLU, CANAN - AYDIN, Ayhan. "Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)". (2021), 647-660. https://doi.org/10.3906/mat-2009-51

APA	KÖROĞLU C, AYDIN A (2021). Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). Turkish Journal of Mathematics, 45(2), 647 - 660. 10.3906/mat-2009-51
Chicago	KÖROĞLU CANAN,AYDIN Ayhan Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). Turkish Journal of Mathematics 45, no.2 (2021): 647 - 660. 10.3906/mat-2009-51
MLA	KÖROĞLU CANAN,AYDIN Ayhan Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). Turkish Journal of Mathematics, vol.45, no.2, 2021, ss.647 - 660. 10.3906/mat-2009-51
AMA	KÖROĞLU C,AYDIN A Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). Turkish Journal of Mathematics. 2021; 45(2): 647 - 660. 10.3906/mat-2009-51
Vancouver	KÖROĞLU C,AYDIN A Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2). Turkish Journal of Mathematics. 2021; 45(2): 647 - 660. 10.3906/mat-2009-51
IEEE	KÖROĞLU C,AYDIN A "Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)." Turkish Journal of Mathematics, 45, ss.647 - 660, 2021. 10.3906/mat-2009-51
ISNAD	KÖROĞLU, CANAN - AYDIN, Ayhan. "Exact and nonstandard finite difference schemes for the Burgers equation B(2, 2)". Turkish Journal of Mathematics 45/2 (2021), 647-660. https://doi.org/10.3906/mat-2009-51