  The purpose of this research work is to employ the Optimal Auxiliary Function
Method (OAFM) for obtaining numerical approximations of time-dependent
nonlinear partial differential equations (PDEs) that arise in many disciplines
of science and engineering. The initial and first approximations of parabolic
nonlinear PDEs associated with initial conditions have been generated by
utilizing this method. Then the Galerkin method is applied to estimate the
coefficients that remain unknown. Finally, the values of the coefficients
generated by the Galerkin method have been inserted into the first
approximation. In each example, all numerical computations and corresponding
absolute errors are provided in schematic and tabular representations. The rate
of convergence attained by the proposed method is depicted in tabular form
