Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri

Zehra Pinar; Hüseyin Kocak; Yasser Daoud

Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri

Year 2018, Volume: 8 Issue: 1, 197 - 202, 01.01.2018

Abstract

Bu çalışma, üçüncü mertebeden reaksiyon terimli dağılım dispersive denkleminin yarı analitik çözümlerini üzerinedir. Son zamanlarda ele alınan problem literatürde tam olarak çözülmüştür. Ayrıca, yarı analitik çözümler, önerilen reaksiyon-dağılım denkleminin çözümünde homotopi temelli yöntemlerin hassasiyetini anlamak için gereklidir. Seçilen pertürbasyon parametreleri ile sembolik hesaplama kullanarak, yarı analitik çözümler, homotopi ve Padé tekniklerinin verimliliğini göstermek için kesin çözümlerle karşılaştırılmaktadır. Elde edilen çözümler dağılımlı ortamda reaksiyon modellemesinde büyük rol oynamaktadır

Keywords

Homotopi analiz metodu, Padé yaklaşımı, Reaksiyon-dağılım denklemi, Yarı-analitik çözümler

References

Baker, GAJr., Graves-Morris, P. 1996. Padé Approximants. Cambridge U.P.
Brezenski, C. 1996. Extrapolation algorithms and Padé approximations. Appl Numer Math, 20 (3): 299–318
Fisher, RA. 1937. The wave of advance of advantageous genes. Ann. Eugenics 7:353-369.
He, JH. 1999. Homotopy perturbation technique. Comput. Methods Appl. Mech. Engng. 178 (3/4) : 257–262.
He, JH. 1998. An approximate solution technique depending upon an artificial parameter. Commun. Nonlinear Sci. Numer. Simulat. 3 (2): 92–97.
He, JH. 1998. Newton-like iteration method for solving algebraic equations. Commun. Nonlinear Sci. Numer. Simulat. 3 (2): 106– 109.
He, JH. 2000. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear Mech, 35 (1): 37–43.
He, JH. 2004. Comparison of homotopy perturbation method and homotopy analysis method. Appl Math Comput 156(2): 527-539.
Jegen, MD., Everett, ME., Schultz, A. 2001. Using homotopy to invert geophysical data. Geophysics 66 (6):1749–1760.
Kocak, H., Pinar, Z. 2017. On solutions of the fifth-order dispersive equations with porous medium type non-linearity. Wave Random Complex Media, DOI:10.1080/17455030.2017 .1367438, 2017.
Kolmogorov, AN., Petrovskii, I. G., Piskunov, NS. 1937. Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem. Bull. Moskov. Gos. Univ., Sect. A, 1:1–26. English. transl. In: Dynamics of Curved Fronts, P. Pelce, Ed., Acad. Press, Inc., New York, 1988, 105– 130.

Semi-analytical solutions of nonlinear equation modelling reaction in a dispersive medium

Year 2018, Volume: 8 Issue: 1, 197 - 202, 01.01.2018

Zehra Pinar Hüseyin Kocak Yasser Daoud

Abstract

This study explores the semi-analytical solutions of the third-order dispersive equation with reaction Fisher-like term. Recently, the proposed problem has been exactly solved in the literature. Additionally, the semi-analytical solutions are needed to understand the sensitivity of homotopy based methods in solving the proposed reaction-dispersion equation. Using symbolic computation with carefully chosen perturbation parameters, the semi-analytical solutions are compared with the exact solutions, in order to show the efficiency of homotopy and Padé techniques. Obtained solutions, which can play key role in modelling reaction in a dispersive medium, are illustrated and discussed.

Keywords

Reaction-dispersion equation, Homotopy Analysis Method, Padé approximation, Semi-analytical solutions

References

Baker, GAJr., Graves-Morris, P. 1996. Padé Approximants. Cambridge U.P.
Brezenski, C. 1996. Extrapolation algorithms and Padé approximations. Appl Numer Math, 20 (3): 299–318
Fisher, RA. 1937. The wave of advance of advantageous genes. Ann. Eugenics 7:353-369.
He, JH. 1999. Homotopy perturbation technique. Comput. Methods Appl. Mech. Engng. 178 (3/4) : 257–262.
He, JH. 1998. An approximate solution technique depending upon an artificial parameter. Commun. Nonlinear Sci. Numer. Simulat. 3 (2): 92–97.
He, JH. 1998. Newton-like iteration method for solving algebraic equations. Commun. Nonlinear Sci. Numer. Simulat. 3 (2): 106– 109.
He, JH. 2000. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Nonlinear Mech, 35 (1): 37–43.
He, JH. 2004. Comparison of homotopy perturbation method and homotopy analysis method. Appl Math Comput 156(2): 527-539.
Jegen, MD., Everett, ME., Schultz, A. 2001. Using homotopy to invert geophysical data. Geophysics 66 (6):1749–1760.
Kocak, H., Pinar, Z. 2017. On solutions of the fifth-order dispersive equations with porous medium type non-linearity. Wave Random Complex Media, DOI:10.1080/17455030.2017 .1367438, 2017.
Kolmogorov, AN., Petrovskii, I. G., Piskunov, NS. 1937. Study of the diffusion equation with growth of the quantity of matter and its application to a biological problem. Bull. Moskov. Gos. Univ., Sect. A, 1:1–26. English. transl. In: Dynamics of Curved Fronts, P. Pelce, Ed., Acad. Press, Inc., New York, 1988, 105– 130.

There are 11 citations in total.

Details

Primary Language	Turkish
Journal Section	Research Article
Authors	Zehra Pinar This is me Hüseyin Kocak This is me Yasser Daoud This is me
Publication Date	January 1, 2018
Published in Issue	Year 2018 Volume: 8 Issue: 1

Cite

APA	Pinar, Z., Kocak, H., & Daoud, Y. (2018). Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri. Karaelmas Fen Ve Mühendislik Dergisi, 8(1), 197-202.
AMA	Pinar Z, Kocak H, Daoud Y. Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri. Karaelmas Fen ve Mühendislik Dergisi. January 2018;8(1):197-202.
Chicago	Pinar, Zehra, Hüseyin Kocak, and Yasser Daoud. “Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri”. Karaelmas Fen Ve Mühendislik Dergisi 8, no. 1 (January 2018): 197-202.
EndNote	Pinar Z, Kocak H, Daoud Y (January 1, 2018) Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri. Karaelmas Fen ve Mühendislik Dergisi 8 1 197–202.
IEEE	Z. Pinar, H. Kocak, and Y. Daoud, “Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri”, Karaelmas Fen ve Mühendislik Dergisi, vol. 8, no. 1, pp. 197–202, 2018.
ISNAD	Pinar, Zehra et al. “Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri”. Karaelmas Fen ve Mühendislik Dergisi 8/1 (January 2018), 197-202.
JAMA	Pinar Z, Kocak H, Daoud Y. Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri. Karaelmas Fen ve Mühendislik Dergisi. 2018;8:197–202.
MLA	Pinar, Zehra et al. “Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 8, no. 1, 2018, pp. 197-02.
Vancouver	Pinar Z, Kocak H, Daoud Y. Dağılımlı Bir Ortamda Doğrusal Olmayan Reaksiyon Model Denkleminin Yarı Analitik Çözümleri. Karaelmas Fen ve Mühendislik Dergisi. 2018;8(1):197-202.