| Title:
|
Approximation of solutions of a difference-differential equation (English) |
| Author:
|
Pachpatte, B. G. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
46 |
| Issue:
|
2 |
| Year:
|
2010 |
| Pages:
|
145-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
approximation of solutions |
| Keyword:
|
difference-differential equation |
| Keyword:
|
Gronwall-Bellman |
| Keyword:
|
integral inequality |
| Keyword:
|
Volterra type |
| Keyword:
|
difference-integral equation |
| Keyword:
|
estimate |
| Keyword:
|
closeness of solutions |
| MSC:
|
34K05 |
| MSC:
|
34K10 |
| MSC:
|
34K40 |
| MSC:
|
65L03 |
| idZBL:
|
Zbl 1240.34295 |
| idMR:
|
MR2684256 |
| . |
| Date available:
|
2010-06-22T22:12:07Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140310 |
| . |
| Reference:
|
[1] Bellman, R., Cooke, K. L.: Differential-Difference Equations.Academic Press, New York, 1963. Zbl 0105.06402, MR 0147745 |
| Reference:
|
[2] Driver, R. D.: Ordinary and Delay Differential Equations.Springer-Verlag, New York-Heidelberg, Appl. Math. Sci. 20, 1977. Zbl 0374.34001, MR 0477368 |
| Reference:
|
[3] Hale, J. K.: Theory of Functional Differential Equations.Springer-Verlag, New York-Heidelberg, Appl. Math. Sci. 3, 1977. Zbl 0352.34001, MR 0508721, 10.1007/978-1-4612-9892-2_3 |
| Reference:
|
[4] Kung, Y.: Delay Differential Equations with Applications in Population Dynamics.Academic Press, Inc., Boston, Math. Sci. Engrg. 191, 1993. MR 1218880 |
| Reference:
|
[5] Pachpatte, B. G.: Inequalities for Differential and Integral Equations.Academic Press, Inc., San Diego, Math. Sci. Engrg. 197, 1998. Zbl 1032.26008, MR 1487077 |
| Reference:
|
[6] Pachpatte, B. G.: Some basic theorems on difference-differential equations.Electron. J. Differential Equations (2008), no. 75, 11pp. Zbl 1172.34041, MR 2411071 |
| Reference:
|
[7] Pachpatte, B. G.: Existence and uniqueness theorems on certain difference-differential equations.Electron. J. Differential Equations (2009), no. 49, 12pp. Zbl 1172.34332, MR 2495854 |
| Reference:
|
[8] Sugiyama, S.: On the boundedness of solutions of difference-differential equations.Proc. Japan Acad. 36 (1960), 456–460. Zbl 0114.04601, MR 0124585 |
| Reference:
|
[9] Sugiyama, S.: On the existence and uniqueness theorems of difference-differential equations.Kōdai Math. Sem. Rep. 12 (1960), 456–460. Zbl 0097.06803, MR 0121552 |
| Reference:
|
[10] Sugiyama, S.: Existence theorems on difference-differential equations.Proc. Japan Acad. 38 (1962), 145–149. Zbl 0105.06501, MR 0144042 |
| . |
