According to the Netwon-Raphson iterative method,first the discrete approximations for surface normal are taken,using finite difference,and then linearize the reflectance function in depth,,instead of and,The new method decreases the complexity and improves the speed of operation greatly,and keeps the shape accuracy.

As for the blind area problem in the process of the hydraulic conveyance,the approximate discretization and power compensation are suggested to be adopted as the solution to simplify the system and to improve its stability and preciseness.

We analytically study soliton excitations in a diatomic chain with different masses and alternating force constants between the nearest neighbors by the means of multiple scales plus quasi discrete approximation method.

Based on approximate models and genetic arithmetic,a scheme for the plane with multi-flaps was proposed to implement the multidisciplinary design optimization(MDO) of full-envelope flight control law and control effectors geometry & their placement.

In this approach, uniform design method was employed to generate the geometric information of samples, whose performances are calculated by CFD technique; the relationship between the geometric information and its performances of samples is mapped by the approximate model constructed by parallel artificial networks (PANN); genetic algorithms is employed to find .

In the light of the huge amount of time-consuming CFD (computational fluid dynamics) calculations during the numerical optimization of a turbo-machinery unit,developed was an optimized design method based on an approximate model.