Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines

Askari, Maysam; Adibi, Hojatollah

doi:10.22034/cmde.2021.44511.1885

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	Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines
Computational Methods for Differential Equations
مقاله 9، دوره 10، شماره 3، مهر 2022، صفحه 686-700 اصل مقاله (5.45 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44511.1885
نویسندگان
Maysam Askari^* ¹؛ Hojatollah Adibi²
¹Department of mathematics, Professor Hesabi Branch, Islamic Azad University, Tafresh, Iran.
²Department of Mathematics, Amirkabir University of Technology, Tehran, Iran.
چکیده
In this article, an efficient method for approximating the solution of the generalized Burgers-Huxley (gB-H) equation using a multiquadric quasi-interpolation approach is considered. This method consists of two phases. First, the spatial derivatives are evaluated by MQ quasi-interpolation, So the gB-H equation is reduced to a nonlinear system of ordinary differential equations. In phase two, the obtained system is solved by using ODE solvers. Numerical examples demonstrate the validity and applicability of the method.
کلیدواژه‌ها
Generalized Burgers-Huxley equation؛ Multiquadric quasi-interpolation؛ Method of lines

مراجع
[1] N. Alinia and M. Zarebnia, A numerical algorithm based on a new kind of tension B-spline function for solving Burgers-Huxley equation, Numer. Algorithms., 82 (2019), 1121–1142. [2] E. Ashpazzadeh, B. Han, and M. Lakestani, Biorthogonal multiwavelets on the interval for numerical solutions of Burgers’ equation, J. Comput. Appl. Math., 317 (2017), 510–534. [3] B. Batiha, M. S. M. Noorani, and I. Hashim, Application of variational iteration method to the generalized Burgers–Huxley equation, Chaos. Solitons. Fractals., 36 (2008), 660–663. [4] R. K. Beatson and M. J. D. Powell, Univariate multiquadric approximation: quasi interpolation to scattered data, Constr. Approx., 8 (1992), 275–288. [5] A. G. Bratsos, A fourth order improved numerical scheme for the generalized Burgers–Huxley equation, Am. J. Comput. Math., 1 (2011), 152–158. [6] M. D. Buhmann, Radial Basis Functions: Theory and implementations, Cambridge University Press, 2003. [7] R. Chen, X. Han, and Z. Wu, A multiquadric quasi-interpolation with linear reproducing and preserving mono- tonicity, J. Comput. Appl. Math., 231 (2009), 517–525. [8] R. Chen and Z. Wu, Applying multiquadric quasi-interpolation to solve Burgers’ equation, Appl. Math. Comput., 172 (2006), 472–484. [9] M. Dehghan, B. Nemati Saray, and M. Lakestani, Mixed finite difference and Galerkin methods for solving Burgers equations using interpolating scaling functions, Math. Methods. Appl. Sci., 37 (2014), 894–912. [10] F. Gao and C. Chi, em Numerical solution of nonlinear Burgers’ equation using high accuracy multi-quadric quasi-interpolation, Appl. Math. Comput., 229 (2014), 414–421. [11] R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res., 176 (1971), 1905–1915. [12] R. L. Hardy, Theory and applications of the multiquadric-biharmonic method, 20 years of discovery 1968-1988, Comput. Math. Appl., 19 (1990), 163–208. [13] I. Hashim, M. S. M. Noorani, and M. R. S. Al-Hadidi, Solving the generalized Burgers-Huxley equation using the Adomian decomposition method, Math. Comput. Model., 43 (2006), 1404–1411. [14] H. N. A. Ismail, K. Raslan, and A. A. A. Rabboh, Adomian Decomposition Method for Burger’s Huxley and Burger’s-Fisher Equations, Appl. Math. Comput., 159 (2004), 291–301. [15] M. Izadi, Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation, Computational Methods for Differential Equations, 8 (2020), 708–732. [16] Z. Jiang and R. Wang, Numerical solution of one-dimensional Sine–Gordon equation using high accuracy multi- quadric quasi-interpolation, Appl. Math. Comput., 218 (2012), 7711–7716. [17] Z. Jiang, R. Wang, C. Zhu and X. Min, High accuracy multiquadricquasi-interpolation, Appl. Math. Model., 35 (2011), 2185–2195. [18] M. El-Kady, S. M. El-Sayed, and H. E. Fathy, Development of Galerkin method for solving the generalized Burger’s- Huxley equation, Math. Probl. Eng., (2013), 1–9. [19] L. Ling, A univariate quasi-multiquadric interpolation with better smoothness, Comput. Math. Appl., 48 (2004), 897–912. [20] L. Ling, Multivariate quasi-interpolation schemes for dimension-splitting multiquadric, Appl. Math. Comput., 161 (2005), 195–209. [21] L. Ma and Z. Wu, Approximation to the k-th derivatives by multiquadric quasi-interpolation, J. Comput. Appl. Math., 231 (2009), 925–932. [22] L. Ma, Z. Wu, Stability of multiquadric quasi-interpolation to approximate high order derivatives, Sci. China Math., 53 (2009), 985–992. [23] M. J. D. Powell, Univariate multiquadric approximation: reproduction of linear polynomials, in: W. Haussman, K. Jetter (Eds.), Multivariate Approximation and Interpolation, Birkhauser Verlag, 1990, 227–240 [24] R. Schaback and Z. Wu, Construction techniques for highly accurate quasi-interpolation operators, J. Approx. theory., 91 (1997), 320–331. [25] S. Shukla and M. Kumar, Error analysis and numerical solution of Burgers-Huxley equation using 3-scale Haar wavelets, Eng. Comput., 36 (2020). [26] B. K. Singh, G. Arora, and M. K. Singh, A numerical scheme for the generalized Burgers–Huxley equation, J. Egyptian Math. Soc., 24 (2016), 629–637. [27] L. Y. Sun and C. G. Zhu, Cubic B-spline quasi-interpolation and an application to numerical solution of generalized Burgers-Huxley equation, Adv. Mech. Eng., 12 (2020), 1–8. [28] R. Wang, X. Min, and Q. Fang, A kind of improved univariate multiquadric quasi-interpolation operators, Comput. Math. Appl., 59 (2010), 451–456. [29] X. Y. Wang, Z. S. Zhu, and Y. K. Lu, Solitary wave solutions of the generalized Burgers-Huxley equation, J. Phys. A: Math. Gen., 23 (1990), 271–274. [30] H. Wu and Y. Duan, Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis–Procesi equations, Appl. Math. Comput., 274 (2016), 83–92. [31] R. Wu, T. Wu, and H. Li, A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction, J. Comput. Appl. Math., 274 (2015), 88–108. [32] Z. Wu and J. P. Liu, Generalized Strang-Fix condition for scattered data quasi-iterpolation, Adv. Comput. Math., 23 (2005), 201–214. [33] Z. Wu and R. Schaback, Shape preserving properties and convergence of univariate multiquadric quasi- interpolation, Acta. Math. Appl. Sin. Engl. Ser., 10 (1994), 441–446. [34] Y. Zhang, X. Liang, and Q. Li, A further research on the convergence of Wu-Schaback’s multi-quadric quasi- interpolation, J. Appl and Computat. Math., 2 (2013), 1–3.
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Numerical investigation of the generalized Burgers-Huxley equation using combination of multiquadric quasi-interpolation and method of lines