Approximation of solutions of a difference-differential equation

B. G. Pachpatte

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 2, page 145-155
  • ISSN: 0044-8753

Abstract

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In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.

How to cite

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Pachpatte, B. G.. "Approximation of solutions of a difference-differential equation." Archivum Mathematicum 046.2 (2010): 145-155. <http://eudml.org/doc/37774>.

@article{Pachpatte2010,
abstract = {In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.},
author = {Pachpatte, B. G.},
journal = {Archivum Mathematicum},
keywords = {approximation of solutions; difference-differential equation; Gronwall-Bellman; integral inequality; Volterra type; difference-integral equation; estimate; closeness of solutions; approximation of solutions; difference-differential equation; Gronwall-Bellman; integral inequality; Volterra type; difference-integral equation; estimate; closeness of solutions},
language = {eng},
number = {2},
pages = {145-155},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Approximation of solutions of a difference-differential equation},
url = {http://eudml.org/doc/37774},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Pachpatte, B. G.
TI - Approximation of solutions of a difference-differential equation
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 2
SP - 145
EP - 155
AB - In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results. Applications to a Volterra type difference-integral equation are also given.
LA - eng
KW - approximation of solutions; difference-differential equation; Gronwall-Bellman; integral inequality; Volterra type; difference-integral equation; estimate; closeness of solutions; approximation of solutions; difference-differential equation; Gronwall-Bellman; integral inequality; Volterra type; difference-integral equation; estimate; closeness of solutions
UR - http://eudml.org/doc/37774
ER -

References

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  1. Bellman, R., Cooke, K. L., Differential-Difference Equations, Academic Press, New York, 1963. (1963) Zbl0105.06402MR0147745
  2. Driver, R. D., Ordinary and Delay Differential Equations, Springer-Verlag, New York-Heidelberg, Appl. Math. Sci. 20, 1977. (1977) Zbl0374.34001MR0477368
  3. Hale, J. K., 10.1007/978-1-4612-9892-2_3, Springer-Verlag, New York-Heidelberg, Appl. Math. Sci. 3, 1977. (1977) Zbl0352.34001MR0508721DOI10.1007/978-1-4612-9892-2_3
  4. Kung, Y., Delay Differential Equations with Applications in Population Dynamics, Academic Press, Inc., Boston, Math. Sci. Engrg. 191, 1993. (1993) MR1218880
  5. Pachpatte, B. G., Inequalities for Differential and Integral Equations, Academic Press, Inc., San Diego, Math. Sci. Engrg. 197, 1998. (1998) Zbl1032.26008MR1487077
  6. Pachpatte, B. G., Some basic theorems on difference-differential equations, Electron. J. Differential Equations (2008), no. 75, 11pp. (2008) Zbl1172.34041MR2411071
  7. Pachpatte, B. G., Existence and uniqueness theorems on certain difference-differential equations, Electron. J. Differential Equations (2009), no. 49, 12pp. (2009) Zbl1172.34332MR2495854
  8. Sugiyama, S., On the boundedness of solutions of difference-differential equations, Proc. Japan Acad. 36 (1960), 456–460. (1960) Zbl0114.04601MR0124585
  9. Sugiyama, S., On the existence and uniqueness theorems of difference-differential equations, Kōdai Math. Sem. Rep. 12 (1960), 456–460. (1960) Zbl0097.06803MR0121552
  10. Sugiyama, S., Existence theorems on difference-differential equations, Proc. Japan Acad. 38 (1962), 145–149. (1962) Zbl0105.06501MR0144042

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