In this paper, two finite difference schemes are presented for initial-boundary value problems of Regularized Long-Wave(RLW) equation. They all have the advantages that there are discrete energies which are conserved....In this paper, two finite difference schemes are presented for initial-boundary value problems of Regularized Long-Wave(RLW) equation. They all have the advantages that there are discrete energies which are conserved. Convergence and stability of difference solutions with order O(h2+τ2) are proved in the energy norm. Numerical experiment results demonstrate the effectiveness of the proposed schemes.展开更多
This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration sch...This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.展开更多
基金The project supported by the national natural science foundation of China (10471023,10572057)
文摘In this paper, two finite difference schemes are presented for initial-boundary value problems of Regularized Long-Wave(RLW) equation. They all have the advantages that there are discrete energies which are conserved. Convergence and stability of difference solutions with order O(h2+τ2) are proved in the energy norm. Numerical experiment results demonstrate the effectiveness of the proposed schemes.
基金supported by National Natural Science Foundation of China under Grant No.10672143the Natural Science Foundation of Henan Province under Grant No.0511022200
文摘This paper focuses on studying a new energy-work relationship numericM integration scheme of nonholonomic Hamiltonian systems. The signal-stage numerical, multi-stage and parallel composition numerical integration schemes are presented. The high-order energy-work relation scheme of the system is constructed by a parallel connection of n multi-stage schemes of order 2, its order of accuracy is 2n. The connection, which is discrete analogue of usual case, between the change of energy and work of nonholonomic constraint forces is obtained for nonholonomie Hamiltonian systems. This paper also gives that there is smaller error of the scheme when taking a large number of stages than a less one. Finally, an applied example is discussed to illustrate these results.
