  In this article, we present the time-space Chebyshev pseudospectral method
(TS-CPsM) to approximate a solution to the generalised Burgers-Fisher (gBF)
equation. The Chebyshev-Gauss-Lobatto (CGL) points serve as the foundation for
the recommended method, which makes use of collocations in both the time and
space directions. Further, using a mapping, the non-homogeneous
initial-boundary value problem is transformed into a homogeneous problem, and a
system of algebraic equations is obtained. The numerical approach known as
Newton-Raphson is implemented in order to get the desired results for the
system. The proposed method's stability analysis has been performed. Different
researchers' considerations on test problems have been explored to illustrate
the robustness and practicality of the approach presented. The approximate
solutions we found using the proposed method are highly accurate and
significantly better than the existing results.
