Abstract:
In this paper, the Lie-Trotter splitting method (LSM) is used to solve the generalized Burgers-Huxley equation (GBHE) numerically. We first establish the local error bounds of approximate solutions of the GBHE with the help of the theory of differential operators in a Banach space. Then we prove the global convergence by using a telescoping identity. At the end, the accuracy of the method is provided by numerical results which are compared with earlier studies.
\Bibitem{CicKor21}
\by Y.~{\v C}i{\v{c}}ek, S.~Korkut
\paper On the numerical solution of the generalized Burgers-Huxley equation by Lie-Trotter splitting method
\jour Sib. Zh. Vychisl. Mat.
\yr 2021
\vol 24
\issue 1
\pages 103--116
\mathnet{http://mi.mathnet.ru/sjvm768}
\crossref{https://doi.org/10.15372/SJNM20210108}
\transl
\jour Num. Anal. Appl.
\yr 2021
\vol 14
\issue 1
\pages 90--102
\crossref{https://doi.org/10.1134/S1995423921010080}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85107553064}
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https://www.mathnet.ru/eng/sjvm768
https://www.mathnet.ru/eng/sjvm/v24/i1/p103
This publication is cited in the following 3 articles:
Mahbubeh Rahimi, Hojatollah Adibi, Majid Amirfakhrian, “Numerical study of nonlinear generalized Burgers–Huxley equation by multiquadric quasi-interpolation and pseudospectral method”, Math Sci, 17:4 (2023), 431
Appanah R. Appadu, Yusuf O. Tijani, “1D Generalised Burgers-Huxley: Proposed Solutions Revisited and Numerical Solution Using FTCS and NSFD Methods”, Front. Appl. Math. Stat., 7 (2022)
Seydaoglu M., Ucar Yu., Kutluay S., “An Efficient Strang Splitting Technique Combined With the Multiquadric-Radial Basis Function For the Burgers' Equation”, Comput. Appl. Math., 40:8 (2021), 309