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<p>This paper introduces a systematic application of the Wavelet-Homotopy Analysis Method (WHAM) for solving the generalized Burgers-Huxley (gB-H) equation, a canonical model that synthesizes nonlinear advection, diffusion, and reaction mechanisms. The proposed WHAM framework integrates boundary-corrected Coiflet wavelets for multiresolution spatial representation with the convergence-controllable homotopy analysis method. A fourth-order Runge-Kutta scheme (RK4) is employed for temporal evolution, enhancing overall accuracy and stability. A rigorous convergence analysis is provided, quantitatively addressing errors from spatial discretization, temporal integration, and the homotopy series. Comprehensive numerical experiments demonstrate that WHAM achieves superior accuracy and long-term stability compared to conventional wavelet-Galerkin (WG) methods, while the associated computational overhead is quantitatively presented and discussed. Notably, the convergence-control parameter offers an effective mechanism for optimizing solution accuracy. The results validate WHAM as a high-order accurate, boundary-aware, and convergence-controllable framework, underscoring its significant potential for analyzing other complex nonlinear evolutionary systems characterized by rogue and shock waves.</p>

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Accurate Coiflet wavelet solution of the generalized Burgers-Huxley equation using the wavelet-homotopy analysis approach

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Hui Wang

摘要

This paper introduces a systematic application of the Wavelet-Homotopy Analysis Method (WHAM) for solving the generalized Burgers-Huxley (gB-H) equation, a canonical model that synthesizes nonlinear advection, diffusion, and reaction mechanisms. The proposed WHAM framework integrates boundary-corrected Coiflet wavelets for multiresolution spatial representation with the convergence-controllable homotopy analysis method. A fourth-order Runge-Kutta scheme (RK4) is employed for temporal evolution, enhancing overall accuracy and stability. A rigorous convergence analysis is provided, quantitatively addressing errors from spatial discretization, temporal integration, and the homotopy series. Comprehensive numerical experiments demonstrate that WHAM achieves superior accuracy and long-term stability compared to conventional wavelet-Galerkin (WG) methods, while the associated computational overhead is quantitatively presented and discussed. Notably, the convergence-control parameter offers an effective mechanism for optimizing solution accuracy. The results validate WHAM as a high-order accurate, boundary-aware, and convergence-controllable framework, underscoring its significant potential for analyzing other complex nonlinear evolutionary systems characterized by rogue and shock waves.