Spectral methods represent a class of advanced techniques renowned for their high-order accuracy and remarkable convergence rates when tackling the approximation of nonlinear problems. This article introduces an enhanced version of the spectral collocation approach, specifically tailored to approximate a generalized Burgers-Fisher (gBF) equation. The focus lies on highlighting the method’s versatility in both temporal and spatial dimensions, leading to exceptional outcomes in terms of error estimation. Applying this method to the given equation results in a system of nonlinear algebraic equations, which is then solved using an iterative approach. Several examples are examined to showcase the method’s effectiveness, demonstrating its ability to overcome challenges inherent in the considered problem while delivering commendable results.

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An Improved Chebyshev Collocation Approximation of the Burgers-Fisher Equation

  • Harvindra Singh,
  • L. K. Balyan

摘要

Spectral methods represent a class of advanced techniques renowned for their high-order accuracy and remarkable convergence rates when tackling the approximation of nonlinear problems. This article introduces an enhanced version of the spectral collocation approach, specifically tailored to approximate a generalized Burgers-Fisher (gBF) equation. The focus lies on highlighting the method’s versatility in both temporal and spatial dimensions, leading to exceptional outcomes in terms of error estimation. Applying this method to the given equation results in a system of nonlinear algebraic equations, which is then solved using an iterative approach. Several examples are examined to showcase the method’s effectiveness, demonstrating its ability to overcome challenges inherent in the considered problem while delivering commendable results.