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Genelleştirilmiş Burgers–Fisher Denkleminin Açık Logaritmik Sonlu Fark Yöntemi ile Sayısal Çözümü

Year 2020, , 752 - 761, 15.07.2020
https://doi.org/10.17714/gumusfenbil.685545

Abstract

Bu
çalışmada genelleştirilmiş Burgers–Fisher denkleminin sayısal çözümleri açık
logaritmik sonlu fark yöntemi (A-LSFY) kullanılarak elde edilmiştir. Elde edilen sayısal çözümler, tam çözümler ve
literatürdeki diğer çalışmalarda elde edilen sayısal çözümlerle
karşılaştırılmıştır. Yapılan bu karşılaştırmalar tablolarla sunulmuştur.

References

  • Chen, X.Y., 2007. Numerical Methods for the Burgers–Fisher Equation. Master Thesis, University of Aeronautics and Astronautics, China.
  • Golbabai, A. ve Javidi, M., 2009. A Spectral Domain Decomposition Approach for the Generalized Burgers–Fisher Equation. Chaos Solitons and Fractals, 39, 385–392.
  • Hammad, D.A. ve El-Azab, M.S., 2015. 2N Order Compact Finite Difference Scheme with Collocation Method for Solving the Generalized Burger’s–Huxley and Burger’s–Fisher Equations. Applied Mathematics and Computation, 258, 296–311.
  • İsmail, H.N.A., Raslan, K. ve Rabboh, A.A.A., 2004. Adomian Decomposition Method for Burgers–Huxley and Burgers–Fisher Equations. Applied Mathematics and Computation, 159, 291–301.
  • İsmail, H.N.A. ve Rabboh, A.A.A., 2004. A Restrictive Pade Approximation for the Solution of the Generalized Fisher and Burgers–Fisher Equation. Applied Mathematics and Computation, 154, 203–210.
  • Javidi, M., 2006. Spectral Collocation Method for the Solution of the Generalized Burger–Fisher Equation. Applied Mathematics and Computation, 174, 45–352.
  • Kaya, D. ve El_Sayed, S.M., 2004. A Numerical Simulation and Explicit Solutions of the Generalized Burger–Fisher Equation. Applied Mathematics and Computation, 152, 403–413.
  • Macias-Diaz, J.E., 2019. On the Numerical and Structural Properties of a Logarithmic Scheme for Diffusion–Reaction Equations. Applied Numerical Mathematics, 140, 104–114.
  • Mickens, R.E. ve Gumel, A.B., 2002. Construction and Analysis of a Non-Standard Finite Difference Scheme for the Burgers–Fisher Equation. Journal of Sound and Vibration, 257 (4), 791–797.
  • Mittal, R.C. ve Tripathi, A., 2015. Numerical Solutions of Generalized Burgers–Fisher and Generalized Burgers–Huxley Gquations Using Collocation of Cubic B-splines. International Journal of Computation Mathematics, 92, 1053–1077.
  • Moghimi, M. ve Hejazi, F.S.A., 2007. Variational Iteration Method for Solving Generalized Burger–Fisher and Burger Equations. Chaos Solitons and Fractals, 33, 1756–1761.
  • Mohammadi, R., 2012. Spline Solution of the Generalized Burgers’-Fisher Equation. Applied Mathematics and Computation, 91, 2189–2215.
  • Wazwaz, A.M., 2005. The Tanh Method for Generalized Forms of Nonlinear Heat Conduction and Burgers–Fisher Equations. Applied Mathematics and Computation, 169, 321–338.
  • Wazzan, L., 2009. A Modified Tanh–Coth Method for Solving the General Burgers–Fisher and the Kuramoto–Sivashinsky Equations. Communications in Nonlinear Science and Numerical Simulation, 14, 2642–2652.
  • Zhang, R., Yu, X. ve Zhao, G., 2012. The Local Discontinuous Galerkin Method for Burger’s–Huxley and Burger’s–Fisher Equations. Applied Mathematics and Computation, 218, 8773–8778.
  • Zhao, T., Li, C., Zang, Z. ve Wu Y., 2012. Chebyshev–Legendre Pseudo-Spectral Method for the Generalised Burgers–Fisher Equation. Applied Mathematical Modelling, 36, 1046–1056.

Numerical Solution of the Generalized Burgers – Fisher Equation with Explicit Logarithmic Finite Difference Method

Year 2020, , 752 - 761, 15.07.2020
https://doi.org/10.17714/gumusfenbil.685545

Abstract

In this study, numerical solutions of
generalized Burgers-Fisher equation are obtained by using explicit
logarithmic finite difference method (E-LFDM). Obtained
numerical solutions are compared by exact solutions and numerical solutions
obtained by other studies in literature. These comparisons are presented with
tables.

References

  • Chen, X.Y., 2007. Numerical Methods for the Burgers–Fisher Equation. Master Thesis, University of Aeronautics and Astronautics, China.
  • Golbabai, A. ve Javidi, M., 2009. A Spectral Domain Decomposition Approach for the Generalized Burgers–Fisher Equation. Chaos Solitons and Fractals, 39, 385–392.
  • Hammad, D.A. ve El-Azab, M.S., 2015. 2N Order Compact Finite Difference Scheme with Collocation Method for Solving the Generalized Burger’s–Huxley and Burger’s–Fisher Equations. Applied Mathematics and Computation, 258, 296–311.
  • İsmail, H.N.A., Raslan, K. ve Rabboh, A.A.A., 2004. Adomian Decomposition Method for Burgers–Huxley and Burgers–Fisher Equations. Applied Mathematics and Computation, 159, 291–301.
  • İsmail, H.N.A. ve Rabboh, A.A.A., 2004. A Restrictive Pade Approximation for the Solution of the Generalized Fisher and Burgers–Fisher Equation. Applied Mathematics and Computation, 154, 203–210.
  • Javidi, M., 2006. Spectral Collocation Method for the Solution of the Generalized Burger–Fisher Equation. Applied Mathematics and Computation, 174, 45–352.
  • Kaya, D. ve El_Sayed, S.M., 2004. A Numerical Simulation and Explicit Solutions of the Generalized Burger–Fisher Equation. Applied Mathematics and Computation, 152, 403–413.
  • Macias-Diaz, J.E., 2019. On the Numerical and Structural Properties of a Logarithmic Scheme for Diffusion–Reaction Equations. Applied Numerical Mathematics, 140, 104–114.
  • Mickens, R.E. ve Gumel, A.B., 2002. Construction and Analysis of a Non-Standard Finite Difference Scheme for the Burgers–Fisher Equation. Journal of Sound and Vibration, 257 (4), 791–797.
  • Mittal, R.C. ve Tripathi, A., 2015. Numerical Solutions of Generalized Burgers–Fisher and Generalized Burgers–Huxley Gquations Using Collocation of Cubic B-splines. International Journal of Computation Mathematics, 92, 1053–1077.
  • Moghimi, M. ve Hejazi, F.S.A., 2007. Variational Iteration Method for Solving Generalized Burger–Fisher and Burger Equations. Chaos Solitons and Fractals, 33, 1756–1761.
  • Mohammadi, R., 2012. Spline Solution of the Generalized Burgers’-Fisher Equation. Applied Mathematics and Computation, 91, 2189–2215.
  • Wazwaz, A.M., 2005. The Tanh Method for Generalized Forms of Nonlinear Heat Conduction and Burgers–Fisher Equations. Applied Mathematics and Computation, 169, 321–338.
  • Wazzan, L., 2009. A Modified Tanh–Coth Method for Solving the General Burgers–Fisher and the Kuramoto–Sivashinsky Equations. Communications in Nonlinear Science and Numerical Simulation, 14, 2642–2652.
  • Zhang, R., Yu, X. ve Zhao, G., 2012. The Local Discontinuous Galerkin Method for Burger’s–Huxley and Burger’s–Fisher Equations. Applied Mathematics and Computation, 218, 8773–8778.
  • Zhao, T., Li, C., Zang, Z. ve Wu Y., 2012. Chebyshev–Legendre Pseudo-Spectral Method for the Generalised Burgers–Fisher Equation. Applied Mathematical Modelling, 36, 1046–1056.
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Gonca Çelikten 0000-0002-2639-2490

Ertan Sürek 0000-0002-9678-4123

Publication Date July 15, 2020
Submission Date February 6, 2020
Acceptance Date June 9, 2020
Published in Issue Year 2020

Cite

APA Çelikten, G., & Sürek, E. (2020). Genelleştirilmiş Burgers–Fisher Denkleminin Açık Logaritmik Sonlu Fark Yöntemi ile Sayısal Çözümü. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 10(3), 752-761. https://doi.org/10.17714/gumusfenbil.685545