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Comparative Study of Some Numerical Methods for the Burgers–Huxley Equation

1
Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port-Elizabeth 6031, South Africa
2
Department of Mathematics, Faculty of Muallim Rıfat Education, Kilis 7 Aralık University, 79000 Kilis, Turkey
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(11), 1333; https://doi.org/10.3390/sym11111333
Received: 19 September 2019 / Revised: 17 October 2019 / Accepted: 19 October 2019 / Published: 24 October 2019
In this paper, we construct four numerical methods to solve the Burgers–Huxley equation with specified initial and boundary conditions. The four methods are two novel versions of nonstandard finite difference schemes (NSFD1 and NSFD2), explicit exponential finite difference method (EEFDM) and fully implicit exponential finite difference method (FIEFDM). These two classes of numerical methods are popular in the mathematical biology community and it is the first time that such a comparison is made between nonstandard and exponential finite difference schemes. Moreover, the use of both nonstandard and exponential finite difference schemes are very new for the Burgers–Huxley equations. We considered eleven different combination for the parameters controlling diffusion, advection and reaction, which give rise to four different regimes. We obtained stability region or condition for positivity. The performances of the four methods are analysed by computing absolute errors, relative errors, L 1 and L errors and CPU time. View Full-Text
Keywords: Burgers–Huxley equation; nonstandard finite difference method; explicit exponential finite difference method; fully implicit exponential finite difference method; absolute error; relative error. Burgers–Huxley equation; nonstandard finite difference method; explicit exponential finite difference method; fully implicit exponential finite difference method; absolute error; relative error.
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Appadu, A.R.; İnan, B.; Tijani, Y.O. Comparative Study of Some Numerical Methods for the Burgers–Huxley Equation. Symmetry 2019, 11, 1333.

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