A Logarithmic Finite Difference Method for Numerical Solutions of the Generalized Huxley Equation

Yıl 2022, Cilt: 7 Sayı: 1, 1 - 6, 30.04.2022

Gonca Çelikten

Öz

In this paper, numerical solutions of generalized Huxley equation are obtained by using a new scheme: Implicit logarithmic finite difference method (I-LFDM). The efficiency of the presented method is illustrated by a numerical example for different cases of parameters which confirm that obtained results are in good agreement with the exact solutions and numerical solutions obtained by some other methods in literature. The method is analyzed by von-Neumann stability analysis method and it is displayed that the method is unconditionally stable.

Anahtar Kelimeler

Generalized Huxley equation, implicit logarithmic finite difference method, von Neumann Satbility analysis

Kaynakça

• [1] Aljaboori, M. A. H. (2018). Exponenetial And Logarithmic Crank-Nicolson Methods For Solving Coupled Burger’s Equations. Misan Journal for Academic Studies, 33, 50-61.
• [2] Batiha, B., Noorani, M.S.M., Hashim, I. (2007). Numerical simulation of the generalized Huxley equation by He’s variational iteration method, Applied Mathematics and Computations, 186: 1322-1325.
• [3] Celikten, G., Göksu, A. and Yagub, G. (2017). Explicit Logarithmic Finite Difference Schemes For Numerical Solution of Burgers Equation. European International Journal of Science and Technology, 6(5), 57-67.
• [4] Celikten, G. (2021). Numerical Solutions of the Modified Burgers Equation by Explicit Logarithmic Finite Difference Schemes. Sohag Journal of Mathematics, 8(3), 73-79.
• [5] Celikten, G. (2020). Logarithmic Finite Difference Methods for Numerical Solutions of Burgers Equation. Erzincan University Journal of Science and Technology, 13(3), 984-994.
• [6] Celikten, G. (2020). Numerical Solution of the Generalized Burgers – Fisher Equation with Explicit Logarithmic Finite Difference Method. Gümüshane University Journal of Science and Technology, 10(3), 752-761.
• [7] El-Azab, M. S., El-Kalla, I. L. and El-Morsy, S. A. (2014). Composite Finite Difference Scheme Applied to a Couple of Nonlinear Evolution Equations. Electronic Journal Of Mathematical Analysis And Applications, 2(2), 254-263.
• [8] Hashemi, S. H., Daniali, H. R. M., Ganji, D. D. (2007). Numerical simulation of the generalized Huxley equation by He’s homotopy perturbation method, Applied Mathematics and Computations, 192: 157-161.
• [9] Hashim, I., Noorani, M. S. M., Batiha, B. (2006). A note on the Adomian decomposition method for the generalized Huxley Equation, Applied Mathematics and Computations, 181: 1439-1445.
• [10] Hemida, K., Mohamed, M. S. (2012). Application of homotopy analysisi method to fractional order generalized Huxley equation, Journal of Applied Functional Analysis, 7(4): 367-372.
• [11] Hilal, N. Injrou, S., Karroum, R. (2020). Exponential finite difference methods for solving Newell–Whitehead–Segel equation, Arabian Journal of Mathematics, 9, 367–379.
• [12] Inan, B.(2016). A New Numerical Scheme for the Generalized Huxley Equation, Bulletin of Mathematical Sciences and Applications, 16: 105-111.
• [13] Inan, B.(2017). Finite difference methods for the generalized Huxley and Burgers-Huxley equations, Kuwait Journal of Science, 44 (3): 20-27.
• [14] Ismail, M.S. and Al-Basyoni, K.S. (2018). A Logarithmic Finite Difference Method for Troesch’s Problem. Applied Mathematics, 9, 550-559.
• [15] Srivastava, V. K., Singh, S. and Awasthi M. K. (2013). Numerical solutions of coupled Burgers' equations by an implicit finite-difference scheme. AIP ADVANCES, 3, 082131.
• [16] Srivastava, V. K., Awasthi, M. K. And Singh, S. (2013). An implicit logarithm finite difference technique for two dimensional coupled viscous Burgers' equation. AIP Advances, 3, 122105.
• [17] Wang, X.Y., Zhu, Z.S., Lu, Y. K. (1990). Solitary wave solutions of the generalized Burgers-Huxley equation, Journal of Physics A: Mathematical and General, 23: 271-274.