High-order compact Padé Scheme with error correction for the GKdV–Burgers–Fisher equation

This paper examines a novel nonlinear wave model, the generalized KdV–Burgers–Fisher (GKdV–Burgers–Fisher) equation, and develops a numerical scheme for accurate approximation of its solutions. Unlike traditional methods that reduce the equation’s order by introducing auxiliary variables, the proposed approach preserves the original form. It uses Taylor series expansions to recast high-order derivative terms as combinations of lower-order ones. A sixth-order Padé approximation then handles the lower-order spatial derivatives, complemented by a consistent fourth-order boundary closure for computing derivative values at the boundaries. Additionally, an error-correction technique approximates the time derivative, yielding a simple and efficient scheme. Theoretical analysis confirms the method’s convergence, and numerical simulations show that the proposed approach is both straightforward and practical.