Taking the Burgers equation as an example,an interval wavelet precise integration method (PIM) for nonlinear PDEs is proposed.The homotopy perturbation method (HPM) for nonlinear problems is adopted.It extends the application of HPM from one dimension to multi-dimensions.As an asymptotic analytical method,it is not sensitive to the time step and is suitable for nonlinear equations.

The implicit symplectic algorithm of Hamilton multibody system with topological tree configuration is studied. The canonical equations of multibody system and Jacobian matrix of RHS of the equations are obtained in the form of matrix.The paper presents algorithm of Jacobian matrix to raise computational efficiency. The implicit symplectic Runge Kutta algorithm is used in solving the canonical equations of multibody system. Numerical results show that the algorithm has higher computational efficiency and can keep computation stable for long time simulation.