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.
Highlights
The excerpt approximation of the Navier-Stokes equation is represented by a prominent nonlinear mathematical model known as Burger’s equation
A fourth-order finite difference method was implemented by Bratsos [29] in a two-time level recurrence relation for the solution of the generalized Burger’sHuxley (gBH) equation
Shukla and Kumar [40] applied the numerical scheme based on the Crank-Nicolson finite difference method in collaboration with the Haar wavelet analysis, to obtain the numerical solution
Summary
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.
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