[1] Al-Rozbayani, A.M. and Al-Hayalie, K.A. Numerical solution of Burger’s-Fisher equation in one-dimensional using finite differences methods, integration 9 (2018), 10.
[2] Bratsos, A.G. A fourth order improved numerical scheme for the gen-eralized Burgers-Huxley equation, Am. J. Comput. Math. 1(03) (2011), 152–158.
[3] Bratsos, A.G. and Khaliq, A.Q.M. An exponential time differencing method of lines for Burgers-Fisher and coupled Burgers equations, J. Comput. Appl. Math. 356 (2019), 182–197.
[4] Chandraker, V., Awasthi, A. and Jayaraj, S. Numerical treatment of Burger-Fisher equation, Procedia Technology 25 (2016), 1217–1225.
[5] Daniel, J.W. and Swartz, B.K. Extrapolated collocation for two-point boundary-value problems using cubic splines, IMA J. Appl. Math. 16(2) (1975), 161–174.
[6] De Boor, C. and Swartz, B. Collocation at Gaussian points, SIAM J. Numer. Anal. 10(4) (1973), 582–606.
[7] Fan, E. Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277(4-5) (2000), 212–218.
[8] Ghasemi, M. A new superconvergent method for systems of nonlinear singular boundary value problems, Int. J. Comput. Math. 90(5) (2013), 955–977.
[9] Ghasemi, M. An efficient algorithm based on extrapolation for the so-lution of nonlinear parabolic equations, Int. J. Nonlinear Sci. Numer. Simul. 19(1) (2018), 37–51.
[10] Golbabai, A. and Javidi, M. A spectral domain decomposition approach for the generalized Burgers–Fisher equation, Chaos Solitons Fractals 39(1) (2009), 385–392.
[11] Hepson, O.E. An extended cubic B–spline finite element method for solving generalized Burgers–Fisher equation, arXiv preprint arXiv:1612.03333 (2016).
[12] Ismail, H.N., Raslan, K. and Abd Rabboh, A.A. Adomian decomposition method for Burger’s–Huxley and Burger’s–Fisher equations, Appl. Math. Comput. 159(1) (2004), 291–301.
[13] Javidi, M. Spectral collocation method for the solution of the generalized Burger–Fisher equation, Appl. Math. Comput. 174(1) (2006), 345–352.
[14] Kadalbajoo, M.K., Tripathi, L.P. and Kumar, A. A cubic B-spline collo-cation method for a numerical solution of the generalized Black–Scholes equation, Math. Comput. Model. 55(3-4) (2012), 1483–1505.
[15] Kaya, D. and El-Sayed, S.M. A numerical simulation and explicit solu-tions of the generalized Burgers-Fisher equation, Appl. Math. Comput. 152(2) (2004), 403–413.
[16] Lighthill, M.J. In surveys in mechanics, Cambridge Cambridge Univer-sity Press, Viscosity effects in sound waves of finite amplitude, 1956.
[17] Lu, B.Q., Xiu, B.Z., Pang, Z.L. and Jiang, X.F. Exact traveling wave solution of one class of nonlinear diffusion equations, Phys. Lett. A, 175(2) (1993), 113–115.
[18] Malik, S.A., Qureshi, I.M., Amir, M., Malik, A.N. and Haq, I. Numer-ical solution to generalized Burgers-Fisher equation using exp-function method hybridized with heuristic computation, PloS one 10(3) (2015), e0121728.
[19] Mickens, R.E. and Gumel, A. Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equation, J. Sound. Vib. 257(4) (2002), 791–797.
[20] Mittal, R.C. and Tripathi, A. Numerical solutions of generalized Burgers–Fisher and generalized Burgers–Huxley equations using colloca-tion of cubic B-splines, Int. J. Comput. Math. 92(5) (2015), 1053–1077.
[21] Moghimi, M. and Hejazi, F.S. Variational iteration method for solving generalized Burger–Fisher and Burger equations, Chaos Solitons Fractals 33(5) (2007), 1756–1761.
[22] Mohammadi, R. Spline solution of the generalized Burgers-Fisher equa-tion, Appl. Anal. 91(12) (2012), 2189–2215.
[23] Murray, J.D. Mathematical biology, Berlin Springer-Verlag, 1989.
[24] Prenter, P.M. Splines and variational methods, New York Wiley-interscience publication, 1975.
[25] Russell, R.D. and Shampine, L.F. A collocation method for boundary value problems, Numer. Math. 19 (1971), 1–28.
[26] Sachdev, P.L. Self-similarity and beyond exact solutions of nonlinear problems, New York, Chapman & Hall/CRC, 2000.
[27] Saeed, U. and Gilani, K. CAS wavelet quasi-linearization technique for the generalized Burger–Fisher equation, Math. Sci. 12(1) (2018), 61–69.
[28] Sangwan, V. and Kaur, B. An exponentially fitted numerical technique for singularly perturbed Burgers-Fisher equation on a layer adapted mesh, Int. J. Comput. Math. 96(7) (2019), 1502–1513.
[29] Sari, M. Differential quadrature solutions of the generalized Burgers-Fisher equation with a strong stability preserving high-order time inte-gration, Math. Comput. Appl. 16(2) (2011), 477–486.
[30] Sari, M., Gürarslan, G. and Dağ, İ. A compact finite difference method for the solution of the generalized Burgers–Fisher equation, Numer. Methods Partial Differ. Equ. 26(1) (2010), 125–134.
[31] Shallu and Kukreja, V.K. An improvised collocation algorithm with spe-cific end conditions for solving modified Burgers equation, Numer. Meth-ods Partial Differ. Equ. 37(1) (2021), 874–896.
[32] Shallu and Kukreja, V.K. Analysis of RLW and MRLW equation using an improvised collocation technique with SSP-RK43 scheme, Wave Motion 105 (2021), 102761.
[33] Shallu and Kukreja, V.K. An improvised collocation algorithm to solve generalized Burgers’-Huxley equation, Arab. J. Math. 11(2) (2022), 379–396.
[34] Shallu, Kumari, A. and Kukreja, V.K. An improved extrapolated collo-cation technique for singularly perturbed problems using cubic B-spline functions, Mediterr. J. Math. 18(4) (2021), 1–29.
[35] Tatari, M., Sepehrian, B. and Alibakhshi, M. New implementation of ra-dial basis functions for solving Burgers‐Fisher equation, Numer. Methods Partial Differ. Equ. 28(1) (2012), 248–262.
[36] Verma, A.K. and Kayenat, S. On the stability of Micken’s type NSFD schemes for generalized Burgers Fisher equation, J. Differ. Equ. Appl. 25(12) (2019), 1706–1737.
[37] Wazwaz, A.M. The tanh method for generalized forms of nonlinear heat conduction and Burgers–Fisher equations, Appl. Math. Comput. 169(1) (2005), 321–338.
[38] Wazwaz, A.M. Analytic study on Burgers, Fisher, Huxley equations and combined forms of these equations, Appl. Math. Comput. 195(2) (2008), 754–761.
[39] Zhao, T., Li, C., Zang, Z. and Wu, Y. Chebyshev–Legendre pseudo-spectral method for the generalised Burgers–Fisher equation, Appl. Math. Model. 36(3) (2012), 1046–1056.
[40] Zhu, C.G. and Kang, W.S. Numerical solution of Burgers–Fisher equa-tion by cubic B-spline quasi-interpolation, Appl. Math. Comput. 216(9) (2010), 2679–2686.
Send comment about this article