| Title:
|
Approximate solutions for integrodifferential equations of the neutral type (English) |
| Author:
|
Pachpatte, B. G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
489-501 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
approximate solutions |
| Keyword:
|
integrodifferential equation |
| Keyword:
|
neutral type |
| Keyword:
|
explicit estimate |
| Keyword:
|
discrete analogues |
| Keyword:
|
dependency of solutions |
| Keyword:
|
closeness of solutions |
| MSC:
|
34A60 |
| MSC:
|
34G20 |
| MSC:
|
34K07 |
| MSC:
|
34K40 |
| MSC:
|
45J05 |
| MSC:
|
45L05 |
| idZBL:
|
Zbl 1224.45015 |
| idMR:
|
MR2741882 |
| . |
| Date available:
|
2010-09-02T14:20:19Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140725 |
| . |
| Reference:
|
[1] Bellman R., Cooke K.L.: On the limit of solutions of differential-difference equations.Proc. Nat. Acad. Sci. 45 (1959), 2026–2028. Zbl 0088.29803, MR 0109243, 10.1073/pnas.45.7.1026 |
| Reference:
|
[2] Bellman R., Cooke K.L.: Differential-Difference Equations.Academic Press, New York, 1963. Zbl 0163.10501, MR 0147745 |
| Reference:
|
[3] Brunner H.: Colloction methods for Volterra integral and related functional differential equations.Cambridge University Press, Cambridge, 2004. MR 2128285 |
| Reference:
|
[4] Buhmann M., Iserles A.: On the dynamics of a discretized neutral equation.IAM J. Numer. Anal. 12 (1992), 339–363. Zbl 0759.65056, MR 1181255, 10.1093/imanum/12.3.339 |
| Reference:
|
[5] Pachpatte B.G.: Inequalities for Differential and Integral Equations.Academic Press, New York, 1998. Zbl 1032.26008, MR 1487077 |
| Reference:
|
[6] Pachpatte B.G.: Inequalities for Finite Difference Equations.Marcel Dekker, Inc., New York, 2002. Zbl 0987.39001, MR 1867845 |
| Reference:
|
[7] Pachpatte B.G.: Integral and Finite Difference Inequalities and Applications.North-Holland Mathematics Studies, 205, Elsevier Science, B.V., Amsterdam, 2006. Zbl 1104.26015, MR 2286291 |
| Reference:
|
[8] Pachpatte B.G.: Implicit type Volterra integrodifferential equation.Tamkang J. Math. 41 (2010), 97–107. MR 2666648 |
| Reference:
|
[9] Sugiyama S.: On the existence and uniqueness theorems of difference-differential equations.Kodai Math. Sem. Rep. 12 (1960), 179–190. Zbl 0097.06803, MR 0121552, 10.2996/kmj/1138844324 |
| Reference:
|
[10] Sugiyama S.: On the boundedness of solutions of difference-differential equations.Proc. Japan Acad. 36 (1960), 456–460. Zbl 0114.04601, MR 0124585 |
| . |
