hp-Legendre-Gauss collocation method for impulsive differential equations

作者：Liang, Hui^*

来源：International Journal of Computer Mathematics, 2017, 94(1): 151-172.

DOI：10.1080/00207160.2015.1099632

• hp-Version
• Legendre-Gauss collocation methods
• impulsive differential equations

The original Legendre-Gauss collocation method is derived for impulsive differential equations, and the convergence is analysed. Then a new hp-Legendre-Gauss collocation method is presented for impulsive differential equations, and the convergence for the hp-version method is also studied. The results obtained in this paper show that the convergence condition for the original Legendre-Gauss collocation method depends on the impulsive differential equation, and it cannot be improved, however, the convergence condition for the hp-Legendre-Gauss collocation method depends both on the impulsive differential equation and the meshsize, and we always can choose a sufficient small meshsize to satisfy it, which show that the hp-Legendre-Gauss collocation method is superior to the original version. Our theoretical results are confirmed in two test problems.

• 出版日期2017-1
• 单位黑龙江大学