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Difference approximations for impulsive differential equations. (English) Zbl 1024.65065
Summary: A convergent difference approximation is obtained for a nonlinear impulsive system in a Banach space.

65L12Finite difference methods for ODE (numerical methods)
65L05Initial value problems for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE
34A37Differential equations with impulses
Full Text: DOI
[1] Bainov, D. D.; Kostadinov, S. I.: Abstract impulsive differential equations. (1995) · Zbl 0822.34013
[2] Berezansky, L.; Braverman, E.; Akça, H.: Boundedness and stability of impulsive perturbed systems in a Banach space. Int. J. Theor. phys. 33, No. 10, 2075-2090 (1994) · Zbl 0814.34047
[3] Hale, J. K.: Theory of functional differential equations. (1977) · Zbl 0352.34001
[4] Lakshmikantham, V.; Bainov, D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[5] Lax, P. D.; Richtmyer, R. D.: Survey of the stability of linear finite difference approximations. Comm. pure appl. Math. 9, 267-293 (1956) · Zbl 0072.08903
[6] Millman, V. D.; Myshkis, A. D.: On the stability of motion in the presence of impulses. Siberian math. J. 1, 233-237 (1960)
[7] Myshkis, A. D.; Samoilenko, A. M.: Systems with impulses in prescribed moments of time. Math. sb. 74, 202-208 (1967)
[8] Richtmyer, R. D.; Morton, K. M.: Difference methods for initial value problems. (1967) · Zbl 0155.47502
[9] A.M. Samoilenko, N.M. Perestyuk, Impulsive Differential Equations, World Scientific Series on Nonlinear Sciences Ser. A, vol. 14, World Scientific, Singapore, 1995 · Zbl 0837.34003
[10] Thompson, R. J.: Difference approximations for inhomogeneous and quasi-linear equations. J. soc. Indust. appl. Math. 12, 189-199 (1964) · Zbl 0124.07203
[11] Thompson, R. J.: Functional-differential equations with unbounded delay in a Banach space. Nonlinear analysis, theory, methods and applications 5, No. 5, 469-473 (1981) · Zbl 0465.34039