Approximate solutions for integrodifferential equations of the neutral type

B. G. Pachpatte

Commentationes Mathematicae Universitatis Carolinae (2010)

• Volume: 51, Issue: 3, page 489-501
• ISSN: 0010-2628

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Abstract

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The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.

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Pachpatte, B. G.. "Approximate solutions for integrodifferential equations of the neutral type." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 489-501. <http://eudml.org/doc/38145>.

@article{Pachpatte2010,
abstract = {The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.},
author = {Pachpatte, B. G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {approximate solutions; integrodifferential equation; neutral type; explicit estimate; discrete analogues; dependency of solutions; closeness of solutions; approximate solution; integro-differential equation; neutral type; explicit estimate; discrete analogue; closeness; integral inequality},
language = {eng},
number = {3},
pages = {489-501},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Approximate solutions for integrodifferential equations of the neutral type},
url = {http://eudml.org/doc/38145},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Pachpatte, B. G.
TI - Approximate solutions for integrodifferential equations of the neutral type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 489
EP - 501
AB - The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.
LA - eng
KW - approximate solutions; integrodifferential equation; neutral type; explicit estimate; discrete analogues; dependency of solutions; closeness of solutions; approximate solution; integro-differential equation; neutral type; explicit estimate; discrete analogue; closeness; integral inequality
UR - http://eudml.org/doc/38145
ER -

References

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5. Pachpatte B.G., Inequalities for Differential and Integral Equations, Academic Press, New York, 1998. Zbl1032.26008MR1487077
6. Pachpatte B.G., Inequalities for Finite Difference Equations, Marcel Dekker, Inc., New York, 2002. Zbl0987.39001MR1867845
7. Pachpatte B.G., Integral and Finite Difference Inequalities and Applications, North-Holland Mathematics Studies, 205, Elsevier Science, B.V., Amsterdam, 2006. Zbl1104.26015MR2286291
8. Pachpatte B.G., Implicit type Volterra integrodifferential equation, Tamkang J. Math. 41 (2010), 97–107. MR2666648
9. Sugiyama S., 10.2996/kmj/1138844324, Kodai Math. Sem. Rep. 12 (1960), 179–190. Zbl0097.06803MR0121552DOI10.2996/kmj/1138844324
10. Sugiyama S., On the boundedness of solutions of difference-differential equations, Proc. Japan Acad. 36 (1960), 456–460. Zbl0114.04601MR0124585

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