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Nonstandard finite‐difference scheme to approximate the generalized Burgers‐Fisher equation
Author(s) -
Namjoo Mehran,
Zeinadini Mehdi,
Zibaei Sadegh
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5283
Subject(s) - mathematics , burgers' equation , scheme (mathematics) , consistency (knowledge bases) , fisher equation , finite difference , finite difference scheme , mathematical analysis , partial differential equation , geometry , real interest rate , monetary economics , economics , interest rate
In this paper, numerical solution of the generalized Burgers‐Fisher (BF) equation is presented on the basis of the nonstandard finite‐difference (NSFD) scheme. At first, two exact finite‐difference schemes for the BF equation are obtained. Afterwards, an NSFD scheme is presented for this equation. The positivity, consistency, and boundedness of the scheme are discussed. The numerical results obtained by the NSFD scheme is compared with the exact solution and some available methods to verify the accuracy and efficiency of the NSFD scheme.