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The purpose of this research work is to employ the Optimal Auxiliary FunctionMethod (OAFM) for obtaining numerical approximations of time-dependentnonlinear partial differential equations (PDEs) that arise in many disciplinesof science and engineering. The initial and first approximations of parabolicnonlinear PDEs associated with initial conditions have been generated byutilizing this method. Then the Galerkin method is applied to estimate thecoefficients that remain unknown. Finally, the values of the coefficientsgenerated by the Galerkin method have been inserted into the firstapproximation. In each example, all numerical computations and correspondingabsolute errors are provided in schematic and tabular representations. The rateof convergence attained by the proposed method is depicted in tabular form

Approximations of Time-Dependent Nonlinear Partial Differential Equations using Galerkin Optimal Auxiliary Function Method