References
- R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
- M.U. Akhmet, On the general problem of stability for impulsive differential equations, J. Math. Anal. Appl. 288 (2003), pp. 182–196. doi: 10.1016/j.jmaa.2003.08.001
- D.D. Bainov and P.S. Simeonov, Systems with Impulsive Effect: Stability, Theory, and Applications, Ellis Horwood, Chichester, 1989.
- H. Brunner and D. Schötzau, hp-discontinuous Galerkin time-stepping for Volterra integrodifferential equations, SIAM. J. Numer. Anal. 44 (2006), pp. 224–245. doi: 10.1137/040619314
- C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer-Verlag, Berlin, 2006.
- X.H. Ding, K.N. Wu, and M.Z. Liu, The Euler scheme and its convergence for impulsive delay differential equations, Appl. Math. Comput. 216 (2010), pp. 1566–1570. doi: 10.1016/j.amc.2010.03.007
- L.Z. Dong, L. Chen, and L.H. Sun, Extinction and permanence of the predator–prey system with stocking of prey and harvesting of predator impulsively, Math. Methods Appl. Sci. 29 (2006), pp. 415–425. doi: 10.1002/mma.688
- B.Y. Guo, Spectral Methods and their Applications, World Scientific, Singapore, 1998.
- B.Y. Guo and Z.Q. Wang, Legendre–Gauss collocation methods for ordinary differential equations, Adv. Complex Math. 30 (2009), pp. 249–280. doi: 10.1007/s10444-008-9067-6
- V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, New York, 1989.
- H. Liang, M.H. Song, and M.Z. Liu, Stability of the analytic and numerical solutions for impulsive differential equations, Appl. Numer. Math. 61 (2011), pp. 1103–1113. doi: 10.1016/j.apnum.2010.12.005
- M.Z. Liu, H. Liang, and Z.W. Yang, Stability of Runge–Kutta methods in the numerical solution of linear impulsive differential equations, Appl. Math. Comput. 192 (2007), pp. 346–357. doi: 10.1016/j.amc.2007.03.044
- V.D. Mil'man and A.D. Myshkis, On the stability of motion in the presence of impulses, Siberian Math. J. 1(2) (1960), pp. 233–237 (Russian).
- X.J. Ran, M.Z. Liu, and Q.Y. Zhu, Numerical methods for impulsive differential equation, Math. Comput. Modelling 48 (2008), pp. 46–55. doi: 10.1016/j.mcm.2007.09.010
- A.M. Samoilenko and N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
- D. Schötzau and C. Schwab, Time discretization of parabolic problems by the hp-version of the discontinuous Galerkin finite element method, SIAM J. Numer. Anal. 38 (2000), pp. 837–875. doi: 10.1137/S0036142999352394
- J. Shen and T. Tang, Spectral and High-Order Methods with Applications, Science Press, Beijing, 2006.
- Z.-Q. Wang and B.-Y. Guo, Legendre–Gauss–Radau collocation method for solving initial value problems of first order ordinary differential equations, J. Sci. Comput. 52 (2012), pp. 226–255. doi: 10.1007/s10915-011-9538-7
- Z.Q. Wang and L.L. Wang, A Legendre–Gauss collocation method for nonlinear delay differential equations, Discrete Contin. Dyn. Syst. Ser. B 3(13) (2010), pp. 685–708. doi: 10.3934/dcdsb.2010.13.685
- Z.H. Zhang and H. Liang, Collocation methods for impulsive differential equations, Appl. Math. Comput. 228 (2014), pp. 336–348. doi: 10.1016/j.amc.2013.11.085