On the stability of Micken's type NSFD schemes for generalized Burgers Fisher equation. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Kumar Verma, Amit; Kayenat, Sheerin
• Is Part Of: Journal of difference equations and applications. Volume 25:Issue 12(2019)
• Page Start: 1706
• Page End: 1737
• Publication Date: 2019-12-02
• Subjects: Non-standard finite difference scheme -- positivity -- boundedness -- exact finite difference scheme -- generalized Burgers Fisher -- nonlinear; 35K61 -- 65M06; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2019.1689236
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: We propose exact finite difference scheme (EFD) for Generalized Burgers Fisher (GBF) Equation w x x = w t + α w θ w x − β w ( 1 − w θ ), 0 ≤ x ≤ 1, t ≥ 0, using solitary wave solution. Moreover a non-standard finite difference (NSFD) scheme is also proposed. The proposed EFD and NSFD scheme works for all θ ∈ N . This scheme preserves the positivity and boundedness properties which is also discussed here. The method is shown to be stable, consistent and first-order accurate in both space and time. Approximate solutions of the GBF equation are obtained using NSFD scheme and in order to show the accuracy, the computed solutions are compared with the exact solution. Comparisons are shown with the other available methods to indicate that our method gives better result. These methods give accurate results even for relatively bigger values of step size.