Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation
Yıl: 2019 Cilt: 12 Sayı: 1 Sayfa Aralığı: 258 - 262 Metin Dili: İngilizce DOI: 10.18185/erzifbed.449161 İndeks Tarihi: 18-01-2021
Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation
Öz: This paper deals with the time-fractional differential-difference Burgers equation1(1 )( ), nnn nd uuu udtDD=+ − +D (0,1). The compact finite differences method (CFD-method) is used for numerical solution of thisproblem. According to the method, we approximate the unknown valuesnu of the desired function bycompact finite differences approximation. As an application, we demonstrate the capabilities of this methodfor identification of various values of order of fractional derivative with distinct two fractional (Riemann–Liouville and Caputo) derivatives. Numerical results show that the proposed version of CFD-method allowsto obtain all data from the initial condition with sufficient high accuracy. AMS (MOS) subject classifications.35R30, 47A52, 35L20
Anahtar Kelime: Zamansal-Kesirli Diferansiyel Fark Burger Denkleminin Sonlu Farklar Yöntemiyle Çözümü
Öz: Bu makalede zamansal-kesirli diferansiyel fark Burger Denklemi 1 (1 )( ), n nn n d u uu u dt D D =+ − + D (0,1) üzerinde durulmuştur. Bu denklemin sayısal çözümü için kompakt sonlu farklar metodu (CFD) kullanılmıştır. Bu metoda göre, kompakt sonlu fark yaklaşımı ile ilgili fonksiyonun bilinmeyen bir n u değerine yaklaşılmıştır. Bir uygulama olarak, farklı iki kesir türevi (Riemann-Liouville ve Caputo) incelenmiştir. Bu iki kesir türev tipi için farklı mertebelerde bulunan değerler karşılaştırılmıştır. Sayısal sonuçlar, CFD yönteminin önerilen versiyonunun, başlangıç koşulundan tüm verilerin yeterli yüksek doğrulukta elde edilmesini sağladığını göstermektedir.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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| APA | POLAT R (2019). Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. , 258 - 262. 10.18185/erzifbed.449161 |
| Chicago | POLAT Refet Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. (2019): 258 - 262. 10.18185/erzifbed.449161 |
| MLA | POLAT Refet Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. , 2019, ss.258 - 262. 10.18185/erzifbed.449161 |
| AMA | POLAT R Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. . 2019; 258 - 262. 10.18185/erzifbed.449161 |
| Vancouver | POLAT R Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. . 2019; 258 - 262. 10.18185/erzifbed.449161 |
| IEEE | POLAT R "Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation." , ss.258 - 262, 2019. 10.18185/erzifbed.449161 |
| ISNAD | POLAT, Refet. "Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation". (2019), 258-262. https://doi.org/10.18185/erzifbed.449161 |
| APA | POLAT R (2019). Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12(1), 258 - 262. 10.18185/erzifbed.449161 |
| Chicago | POLAT Refet Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 12, no.1 (2019): 258 - 262. 10.18185/erzifbed.449161 |
| MLA | POLAT Refet Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.12, no.1, 2019, ss.258 - 262. 10.18185/erzifbed.449161 |
| AMA | POLAT R Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2019; 12(1): 258 - 262. 10.18185/erzifbed.449161 |
| Vancouver | POLAT R Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2019; 12(1): 258 - 262. 10.18185/erzifbed.449161 |
| IEEE | POLAT R "Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 12, ss.258 - 262, 2019. 10.18185/erzifbed.449161 |
| ISNAD | POLAT, Refet. "Finite Difference Solution to the Time-Fractional Differential-Difference Burgers Equation". Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 12/1 (2019), 258-262. https://doi.org/10.18185/erzifbed.449161 |
