In this paper, the operational matrix with Legendre polynomials method will be implemented to get the approximate solution for the nonlinear thin film flow (NTFF) of third grade problem. This method provides an approximate solution by converting the nonlinear differential equation into nonlinear algebraic equations system which can be solved by using Mathematica® 10. To illustrate the accuracy and efficiency of the proposed method, the maximum error remainder was calculated. The results obtained from using the proposed method have proven to be accurate, reliable and effective. In addition, the approximate solution is compared with the fourth order Runge-Kutta method (RK4) and good agreement has been achieved.

本文将利用勒让德多项式的运算矩阵来实现，以解决三级问题的非线性薄膜流（NTFF）的近似解。通过将非线性微分方程转换为非线性代数方程组，可以使用Mathematica®10求解该方法，从而提供了一种近似解决方案。为说明该方法的准确性和效率，计算了最大误差余量。使用所提出的方法获得的结果已被证明是准确，可靠和有效的。此外，将近似解与四阶Runge-Kutta方法（RK4）进行了比较，并取得了良好的一致性。