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

Year 2020, , 752 - 761, 15.07.2020

Gonca Çelikten , Ertan Sürek

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.

Keywords

Açık Logaritmik Sonlu Fark Yöntemi (A-LSFY), Genelleştirilmiş Burgers–Fisher Denklemi, Logaritmik Sonlu Fark Yöntemi

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

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.

Keywords

Explicit Logarithmic Finite Difference Method (E-LFDM), Generalized Burgers–Fisher Equation, Logarithmic Finite Difference Method

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.