VIM-based dynamic sparse grid approach to partial differential equations.
Combining the variational iteration method (VIM) with the sparse grid theory, a dynamic sparse grid approach for nonlinear PDEs is proposed in this paper. In this method, a multilevel interpolation operator is constructed based on the sparse grids theory firstly. The operator is based on the linear combination of the basic functions and independent of them. Second, by means of the precise integration method (PIM), the VIM is developed to solve the nonlinear system of ODEs which is obtained from the discretization of the PDEs. In addition, a dynamic choice scheme on both of the inner and external grid points is proposed. It is different from the traditional interval wavelet collocation method in which the choice of both of the inner and external grid points is dynamic. The numerical experiments show that our method is better than the traditional wavelet collocation method, especially in solving the PDEs with the Nuemann boundary conditions.
College of Information and Electrical Engineering, China Agricultural University, P.O. Box 53, East Campus, 17 Qinghua Donglu Road, Haidian District, Beijing 100083, China.
Shu-Li
SL
Mei
D000465:Algorithms; D000704:Analysis of Variance; D003198:Computer Simulation; D015233:Models, Statistical; D009716:Numerical Analysis, Computer-Assisted