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Abstract
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The KdV–Burgers–Fisher equation is a higher-order nonlinear partial differential equation that models complex physical phenomena such as fluid dynamics, wave propagation, chemical reactions, and nonlinear dispersive systems, combining dispersion, dissipation, and reaction effects. Its nonlinear and higher-order structure makes analytical solutions rare or intractable, and traditional numerical methods often face challenges including instability, low accuracy, and high computational cost, especially for long-time simulations or steep gradients. This creates a strong necessity for robust and accurate numerical methods capable of efficiently resolving the equation’s complex dynamics. The B-spline collocation method, known for its high-order smoothness, local support, and flexibility, provides a suitable framework for approximating the solution, while a thorough stability assessment ensures the reliability of the computed results. The importance of this research lies in establishing a precise, stable, and computationally efficient approach for analyzing the KdV–Burgers–Fisher equation, thereby contributing to both theoretical understanding and practical modeling in applied mathematics and engineering.
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