In this paper, the laminar boundary layer flow over a flat plate, governed by the Prandtl equations, has been studied numerically. The problem is a dimensionless third-order system of nonlinear ordinary differential equations which arises in boundary layer flow. This system is solved using an orthogonal basis for the space of cubic splines (O-splines), as an approximation tool. Some new properties of O-splines have been explored. Also, more accurate values for the initial value of the second derivative of the Falkner–Skan equation are obtained as an initial value inverse problem. Using the new initial values, the problem becomes a first-order system of ordinary differential equations which is solved by the RK45 method and the results are compared with the presented method.

在本文中，对平板上的层流边界层流动进行了数值研究，该流动由 Prandtl 方程控制。问题是边界层流动中出现的非线性常微分方程的无量纲三阶系统。该系统使用三次样条（O 样条）空间的正交基作为近似工具求解。已经探索了 O 样条的一些新特性。此外，Falkner-Skan 方程二阶导数的初始值的更准确值作为初始值逆问题获得。使用新的初始值，该问题成为一阶常微分方程组，通过RK45方法求解，并将结果与​​提出的方法进行比较。