应用人工神经网络求解边界层微分方程

Solving Boundary Layer Differential Equations with Artificial Neural Network

打靶法是一种将常微分方程边值问题转化为初值问题求解的方法,分析和计算表明:打靶的过程可用优化算法实现.应用Hopfield人工神经网络算法求解了沿等壁温竖壁自然对流层流边界微分方程,与其他几种优化算法比较,其计算精度较高.应用解非线性方程的Newton法和拟Newton法求解该问题时,初值选择存在不可行区域,而优化算法对初值选择要求较低.

Boundary value ordinary differential equations are often solved with shooting method to transfer the problem into initial value problem. Detailed analysis and calculation show that the process of ＂ shooting＂ can be implemented with optimization algorithms. Hopfield artificial neural networks algorithm is used in solving laminar free convection boundary layer equations with fluid flow along vertical plate with constant temperature. Compared with the results form other optimization algorithms, Hopfield artificial neural networks algorithm is feasible in solving such problem. It is worthwhile to notice that there exists a non-feasible region in using Newton algorithm or quasi-Newton algorithm for solving free convection boundary layer equations. Optimization algorithms are not sensitive to initial values in solving these equations. design; shooting method