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<p>In this paper, we explore a new, accurate, and efficient finite difference scheme for solving the KdV-Burgers-Fisher equation numerically. To handle the high-order derivative terms in the model, we reformulate them as first-order derivatives, thereby alleviating concerns related to numerical stability. The spatial first-order derivative is discretized utilizing a sixth-order Padé scheme, while the temporal discretization employs a method that integrates corrections for truncation error residuals. Furthermore, we perform a theoretical convergence analysis using energy methods for the nonlinear scheme. Additionally, we conduct dispersion and dissipation analysis via Fourier analysis methods for the linearized steady-state equation, with numerical verification of phase velocity and amplitude decay rate to evaluate wave propagation. Numerical experiments show that the proposed method delivers excellent performance and accuracy.</p>

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High-order reformulation and convergence analysis of a finite difference scheme for the KdV-Burgers-Fisher equation

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Mengling Wu,
  • Can Ma,
  • Kejia Pan,
  • Hongling Hu

摘要

In this paper, we explore a new, accurate, and efficient finite difference scheme for solving the KdV-Burgers-Fisher equation numerically. To handle the high-order derivative terms in the model, we reformulate them as first-order derivatives, thereby alleviating concerns related to numerical stability. The spatial first-order derivative is discretized utilizing a sixth-order Padé scheme, while the temporal discretization employs a method that integrates corrections for truncation error residuals. Furthermore, we perform a theoretical convergence analysis using energy methods for the nonlinear scheme. Additionally, we conduct dispersion and dissipation analysis via Fourier analysis methods for the linearized steady-state equation, with numerical verification of phase velocity and amplitude decay rate to evaluate wave propagation. Numerical experiments show that the proposed method delivers excellent performance and accuracy.