The space distributed-order constitution relationship is firstly formulated to study the flow and heat transfer in the boundary layer. The distributed-order boundary layer equations are derived and approximated by a multi-space fractional order ones, which are then solved by the implicit difference schemes. By comparing the analytical solutions of special boundary conditions, the validity of the present numerical method is examined. Then, the stability and convergence of the implicit finite difference scheme are analysed systematically. Finally, we present two practical examples to illustrate the effectiveness of our numerical method. Furthermore, the numerical technique in this study can be extended to others distributed-order boundary layer models.

首先建立了空间分布顺序的构成关系，以研究边界层中的流动和传热。通过多空间分数阶方程推导并近似了分布阶边界层方程，然后通过隐式差分方案对其进行求解。通过比较特殊边界条件的解析解，检验了本数值方法的有效性。然后，系统地分析了隐式有限差分格式的稳定性和收敛性。最后，我们给出两个实际的例子来说明我们的数值方法的有效性。此外，本研究中的数值技术可以扩展到其他分布式边界层模型。