Abstract
A fourth-order B-spline collocation method has been applied for numerical study of Burgers–Fisher equation, which illustrates many situations occurring in various fields of science and engineering including nonlinear optics,gas dynamics, chemical physics, heat conduction, and so on. The present method is successfully applied to solve the Burgers–Fisher equation taking into consideration various parametric values. The scheme is found to be convergent. Crank–Nicolson scheme has been employed for the discretization. Quasi-linearization technique has been employed to deal with the nonlinearity of equations. The stability of the method has been discussed using Fourier series analysis (von Neumann method), and it has been observed that the method is unconditionally stable. In order to demonstrate the effectiveness of the scheme, numerical experiments have been performed on various examples. The solutions obtained are compared with results available in the literature, which shows that the proposed scheme is satisfactorily accurate and suitable for solving such problems with minimal computational efforts.
Highlights
We consider the following Burgers–Fisher equation of the form v − 2v + v v + v(1 − v) = 0, t x2 x (1)a ≤ x ≤ b and t ≥ 0 where and are advection and source/sink constants
1 Department of Mathematics, DEI Dayalbagh, Agra, UP 282005, India v(b, t) = g1(t). This manuscript deals with the numerical solution of Burgers–Fisher equation, which is nonlinear and parabolic in nature
It describes the mathematical model of many physical situations occurring in various fields of science and engineering such as heat conduction, gas dynamics, chemical physics and nonlinear optics
Summary
Fisher’s equation in its initial stages is extensively worked upon, and its solutions are given by various analytical and numerical methods [4,5,6,7,8,9,10]. Various numerical and analytical methods have been used by various researchers to deal with the Burgers–Fisher equation.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
