A Hp - Legendre - Gauss - Radau Spectrum Configuration Method For Impulsive Differential Equations

A new hp-version spectral collocation method is presented to research impulsive differential equations, and its convergence is analyzed. It is proved that this kind of collocation method is of spectral accuracy. In the different fields of real life, the mathematical model of impulsive differential equations containing impulsive phenomenon can be found, such as economics, biology, physics, medicine, etc.Firstly, the present situation of impulsive differential equations is described, and the spectral methods for differential equations with initial value conditions are briefly stated. Nextly, Legendre-Gauss-Radau spectral collocation scheme for im-pulsive differential equation is given out, and the error of this scheme is analyzed. It is proved that Legendre-Gauss-Radau spectral collocation method is of spectral accuracy. Then, hp-Legendre-Gauss-Radau spectral collocation scheme for impul-sive differential equation is also derived, and its convergence is analyzed accordingly. It is proved that hp-Legendre-Gauss-Radau spectral collocation method is of also spectral accuracy. Finally, the correctness of the conclusions given in this thesis are investigated by numerical examples.