Numerical Approximation of Generalized Burger’s-Fisher and Generalized Burger’s-Huxley Equation by Compact Finite Difference Method

Abstract

In this work, computational analysis of generalized Burger’s-Fisher and generalized Burger’s-Huxley equation is carried out using the sixth-order compact finite difference method. This technique deals with the nonstandard discretization of the spatial derivatives and optimized time integration using the strong stability-preserving Runge-Kutta method. This scheme inculcates four stages and third-order accuracy in the time domain. The stability analysis is discussed using eigenvalues of the coefficient matrix. Several examples are discussed for their approximate solution, and comparisons are made to show the efficiency and accuracy of CFDM6 with the results available in the literature. It is found that the present method is easy to implement with less computational effort and is highly accurate also.

[Retracted] A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model

“…Like any approximation, finite difference schemes have their limitations such as oscillations and diffusion especially at points of discontinuity. Another issue that FDM runs into is that mass is only conserved when the grid spacing goes to zero and they struggle with irregular geometry [2,10]. Usually, a FDM's grid looks like the following (Figure 1).…”

Developing a Robust Bioventing Model

“…FDM, in the same way as any other approximation, has certain limitations, including oscillations and diffusion, particularly at discontinuous points. Additionally, FDM may encounter issues with conserving mass since it is mass conservative only when the grid spacing goes to zero and may have difficulty handling irregular shapes [26,27].…”