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High‐order finite difference schemes for the solution of the generalized Burgers–Fisher equation
Author(s) -
Sari Murat,
Gürarslan Gürhan,
Zeytinoğlu Asuman
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1360
Subject(s) - taylor series , mathematics , burgers' equation , order (exchange) , fisher equation , order of accuracy , series (stratigraphy) , space (punctuation) , exact solutions in general relativity , finite difference , finite difference method , scheme (mathematics) , partial differential equation , mathematical analysis , computer science , method of characteristics , paleontology , finance , real interest rate , monetary economics , economics , biology , interest rate , operating system
Abstract Up to tenth‐order finite difference (FD) schemes are proposed in this paper to solve the generalized Burgers–Fisher equation. The schemes based on high‐order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth‐order FD schemes in space and fourth‐order Runge–Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the efficiency and high‐order accuracy of the present methods. The produced results are also seen to be more accurate than some available results given in the literature. Comparisons showed that there is very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present methods are seen to be very good alternatives to some existing techniques for such realistic problems. Copyright © 2009 John Wiley & Sons, Ltd.