Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem

Kukreja, Vijay Kumar; ., Shallu

doi:10.22034/cmde.2024.49824.2071

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	Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem
Computational Methods for Differential Equations
مقاله 16، دوره 13، شماره 2، خرداد 2025، صفحه 578-591 اصل مقاله (2.46 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.49824.2071
نویسندگان
Vijay Kumar Kukreja^* ؛ Shallu .
Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Punjab, India.
چکیده
This study employs the cubic B-spline collocation strategy to address the solution challenges posed by the nonlinear generalized Burgers-Fisher’s equation (gBFE), with some improvisation. This approach incorporates refinements within the spline interpolants, resulting in enhanced convergence rates along the spatial dimension. Temporal integration is achieved through the Crank-Nicolson methodology. The stability of the technique is assessed using the rigorous von Neumann method. Convergence analysis based on Green’s function reveals a fourth-order convergence along the space domain and a second-order convergence along the temporal domain. The results are validated by taking a number of examples. MATLAB 2017 is used for computational work.
کلیدواژه‌ها
Burgers-Fisher’s equation؛ B-splines collocation method؛ Crank Nicolson؛ Convergence analysis؛ Stability analysis

مراجع
[1] M. J. Ablowitz and A. Zeppetella, Explicit solutions of Fisher’s equation for a special wave speed, Bull. Math, Biol., 41(6) (1979), 835-840. [2] G. Arora and V. Joshi, A computational approach for solution of one dimensional parabolic partial differential equation with application in biological processes, Ain Shams Eng. J., 9(4) (2018), 1141-1150. [3] G. Arora and G. S. Bhatia, A meshfree numerical technique based on radial basis function pseudospectral method for Fishers equation, Int. J. Nonlinear. Sci. Num. Simu., 21(1) (2020), 37-49. [4] S. Arora, R. Jain, and V. K. Kukreja, A robust Hermite spline collocation technique to study generalized BurgersHuxley equation, generalized Burgers-Fisher equation and Modified Burgers equation, J. Ocean Eng. Sci., (2022). [5] A. G. Bratsos, A fourth order improved numerical scheme for the generalized BurgersHuxley equation, Am. J. Comput. Math., 1(03) (2011), 152-158. [6] A. G. Bratsos and A. Q. M. Khaliq, An exponential time differencing method of lines for Burgers-Fisher and coupled Burgers equations, J. Comput. Appl. Math., 356 (2019), 182-197. [7] J. M. Burgers, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mechn., 1 (1948), 171-199. [8] C. De Boor and B. Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10(4) (1973), 582-606. [9] E. Fan, Extended tanh-function method and its applications to nonlinear equations Phys. Lett. A, 277(4-5) (2000), 212-218. [10] R. A. Fisher, The wave of advance of advantageous genes, Ann. Eugen., 7(4) (1937), 355-369. [11] A. Golbabai and M. Javidi, A spectral domain decomposition approach for the generalized BurgersFisher equation, Chaos Solitons Fractals, 39(1) (2009), 385-392. [12] M. Hussain and S. Haq, Numerical solutions of strongly non-linear generalized BurgersFisher equation via meshfree spectral technique, Int. J. Comput. Math., 98(9) (2021), 1727-1748. [13] H. N. Ismail, K. Raslan, and A. A. Abd Rabboh, Adomian decomposition method for Burger’sHuxley and Burger’sFisher equations, Appl. Math. Comput., 159(1) (2004), 291-301. [14] M. Javidi, Spectral collocation method for the solution of the generalized BurgerFisher equation, Appl. Math. Comput., 174(1) (2006), 345-352. [15] R. Kaur, Shallu, S. Kumar, and V. K. Kukreja, Numerical approximation of generalized Burgers-Fisher and generalized Burgers-Huxley equation by compact finite difference method, Adv. Math. Phys., (2021), 1-17. [16] D. Kaya and S. M. El-Sayed, A numerical simulation and explicit solutions of the generalized Burgers-Fisher equation, Appl. Math. Comput., 152(2) (2004), 403-413. [17] J. Mendoza and C. Muriel, New exact solutions for a generalised Burgers-Fisher equation, Chaos, Solitons & Fractals, 152 (2021), 111360. [18] R. C. Mittal and A. Tripathi, Numerical solutions of generalized BurgersFisher and generalized BurgersHuxley equations using collocation of cubic B-splines, Int. J. Comput. Math, 92(5) (2015), 1053-1077. [19] M. Namjoo, M. Zeinadini, and S. Zibaei, Nonstandard finitedifference scheme to approximate the generalized BurgersFisher equation, Math. Mthd. Appl. Sci, 41(17) (2018), 8212-8228. [20] P. M. Prenter, Splines and Variational Methods, New York: Wiley-interscience publication, (1975). [21] U. Saeed and K. Gilani, CAS wavelet quasi-linearization technique for the generalized BurgerFisher equation, Math. Sci., 12(1) (2018), 61-69. [22] V. Sangwan and B. Kaur, 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. [23] M. Sari, G. Grarslan, and . Da, A compact finite difference method for the solution of the generalized BurgersFisher equation, Numer. Methods Partial Differ. Equ., 26(1) (2010), 125-134. [24] Shallu, A. Kumari, and V. K. Kukreja, An improved extrapolated collocation technique for singularly perturbed problems using cubic B-spline functions, Mediterr. J. Math., 18(4) (2021), 1-29. [25] Shallu and V. K. Kukreja, An improvised collocation algorithm with specific end conditions for solving modified Burgers equation, Numer. Methods Partial Differ. Equ., 37(1) (2021), 874-896. [26] Shallu and V. K. Kukreja, Analysis of RLW and MRLW equation using an improvised collocation technique with SSP-RK43 scheme, Wave Motion (2021), 102761. [27] Y. Shang and Q. Chen, The generalized ColeHopf transformation for a generalized BurgersFisher equation with spatiotemporal variable coefficients, Appl. Math. Lett., 117 (2021), 107074. [28] M. Tamsir, N. Dhiman, and V. K. Srivastava, Cubic trigonometric B-spline differential quadrature method for numerical treatment of Fishers reaction-diffusion equations, Alex. Eng. J., 57(3) (2018), 2019-2026. [29] M. Tamsir, V. K. Srivastava, N. Dhiman, and A. Chauhan, Numerical computation of nonlinear Fishers reaction-diffusion equation with exponential modified cubic B-spline differential quadrature method, Int. J. Comput. Math., 4(1) (2018), 1-13. [30] M. Tatari, B. Sepehrian, and M. Alibakhshi, New implementation of radial basis functions for solving BurgersFisher equation, Numer. Methods Partial Differ. Equ., 28(1) (2012), 248-262. [31] A. K. Verma and S. Kayenat, On the stability of Micken’s type NSFD schemes for generalized Burgers Fisher equation, J. Differ. Equ. Appl., 25(12) (2019), 1706-1737. [32] A. M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and BurgersFisher equations, Appl. Math. Comput., 169(1) (2005), 321-338.
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Highly accurate spline collocation technique for the numerical solution of generalized Burgers-Fisher’s problem