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

翻译：本研究旨在利用最优辅助函数方法（OAFM）获取科学与工程多个学科中出现的时间相关非线性偏微分方程（PDEs）的数值近似解。通过该方法，生成了与初始条件相关的抛物型非线性偏微分方程的零阶和一阶近似；随后应用Galerkin方法估计待定系数，并将Galerkin方法所得系数值代入一阶近似。每个算例中，所有数值计算及对应的绝对误差均以示意图和表格形式呈现。所提方法的收敛速率以表格形式展示。