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hp-Legendre–Gauss collocation method for impulsive differential equations

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ABSTRACT 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… Click to show full abstract

ABSTRACT 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.

Keywords: impulsive differential; legendre gauss; method; gauss collocation; collocation method

Journal Title: International Journal of Computer Mathematics
Year Published: 2017

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