For obtaining numerical solutions of the system of ordinary differential equations (ODEs) of third order, a new numerical technique is proposed by using operational matrices of Bernstein polynomials. These operational matrices can be utilized to solve different problems of integral and differential equations. The System of third-order ODEs occur in various physical and engineering models. In this paper, an iterative algorithm is constructed by using operational matrices of Bernstein polynomials for solving the system of third order ODEs. The proposed technique provides a numerical solution by discretizing the system to a system of algebraic equations which can be solved directly. The method will be verified by using appropriate examples which are arising in Physics and some Engineering problems. The comparison of approximate and exact solution of the given examples is demonstrated with the help of tables and graphs.

为了获得三阶常微分方程组（ODE）的数值解，提出了一种使用伯恩斯坦多项式的运算矩阵的新数值技术。这些运算矩阵可用于解决积分方程和微分方程的不同问题。三阶ODE系统出现在各种物理和工程模型中。本文利用伯恩斯坦多项式的运算矩阵构造了一个迭代算法来求解三阶常微分方程组。所提出的技术通过将系统离散化为可以直接求解的代数方程组，从而提供了数值解。将通过使用在物理和一些工程问题中出现的适当示例来验证该方法。