With reductive perturbation method,a Kor tweg-de Vries equat ion is derived,which is easier to solve than the original form equation of nonli near vibrating string.

By using reductive perturbation method, super KdV equations are changed into ordinary KdV equations, small amplitude perturbation solutions are obtained.

A real-time algorithm, called reduced-basis method (RBM), was firstly introduced to the analysis of truck frame.

A real-time algorithm,called reduced-basis method(RBM),was applied to solve the forward problem herein.

Using reduced-basis method (RBM), design parameters are needed to separated from the linear elastic operator (stiffness matrix, mass matrix, and loads), which is time-consuming.

A new texture reduction algorithm not requiring the size of the texture be the power of 2 is presented, and the new reduction algorithm is applied to finding the column pivot and determining the row index of the column pivot in Gaussian elimination method.

Matrix perturbation methods for eigenvalue analysis of vibration of compressible fluid-solid;

A perturbation method for weakly damped systems repeated eigenvalues;

An analytical solution to tunnels with over-under-excavated surface based on perturbation method;