| Title:
|
On modification of Samoilenko's numerical-analytic method of solving boundary value problems for difference equations (English) |
| Author:
|
Kwapisz, Marian |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
133-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper a modification of Samoilenko's numerical analytic method is adapted for solving of boundary value problems for difference equation. Similarly to the case of differential equations it is shown that the considered modification of the method requires essentially less restrictive condition-then the original method-for existence and uniqueness of solution of auxiliary equations which play a crucial role in solving the boundary value problems for difference equations. (English) |
| Keyword:
|
difference equations |
| Keyword:
|
boundary value problems |
| Keyword:
|
numerical methods |
| Keyword:
|
method of successive approximations |
| MSC:
|
39A10 |
| MSC:
|
39A70 |
| MSC:
|
65Q05 |
| idZBL:
|
Zbl 0786.65116 |
| idMR:
|
MR1202749 |
| DOI:
|
10.21136/AM.1993.104540 |
| . |
| Date available:
|
2008-05-20T18:45:15Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104540 |
| . |
| Reference:
|
[1] R. P. Agarval: On multipoint boundary value problems for discrete equations.J. Math. Anal. Appl. 96(1983), 520-534. MR 0719333 |
| Reference:
|
[2] R. P. Agarval: Initial-value methods for discrete boundary value problems.J. Math. Anal. Appl. 100 (1984), 513-529. MR 0743339, 10.1016/0022-247X(84)90099-4 |
| Reference:
|
[3] R. P . Agarval R. C. Gupta: A new shooting method for multi-point boundary value problems.J. Math. Anal. Appl. 112 (1985), 210-220. MR 0812803, 10.1016/0022-247X(85)90286-0 |
| Reference:
|
[4] A. Augustynowicz M. Kwapisz: On a numerical-analytic method of solving of boundary value problem for functional-differential equation of neutral type.Mathem. Nachrichten 145 (1990), 255-269. MR 1069034, 10.1002/mana.19901450120 |
| Reference:
|
[5] P. W. Eloe: A boundary value problem for a system of difference equations.Nonlinear Anal. 7 (1983), 813-820. Zbl 0518.39002, MR 0709036, 10.1016/0362-546X(83)90059-7 |
| Reference:
|
[6] J. Henderson: Existence theorems for boundary value problems for nth order nonlinear difference equations.SIAM J. Math. Anal. 20 (1989), 468-478. Zbl 0671.34017, MR 0982673, 10.1137/0520032 |
| Reference:
|
[7] M. Kwapisz: Some existence and uniqueness results for boundary value problems for difference equations.Applicable Analysis 37 (1990), 169-182. Zbl 0678.39001, MR 1116165, 10.1080/00036819008839945 |
| Reference:
|
[8] M. Kwapisz: On boundary value problems for difference equations.J. Math. Anal. Appl. 157 (1991), 254-270. Zbl 0729.39001, MR 1109455, 10.1016/0022-247X(91)90148-S |
| Reference:
|
[9] M. Kwapisz: Some remarks on integral equations arising in applications of numerical-analytic method of solving of boundary value problems.Ukrain. Mathem. Journal (44)1 (1992), 128-132. MR 1185068 |
| Reference:
|
[10] M. Kwapisz: On modifications of the integral equation of Samoilenko's numerical- analytic method of solving boundary value problems.Math. Nachr. 157(1992), 125-135. MR 1233052, 10.1002/mana.19921570126 |
| Reference:
|
[11] M. Kwapisz: Elements of the Theory of Recurrent Equations.The Gdańsk University Publications, Gdańsk, 1983. (In Polish.) |
| Reference:
|
[12] V. Lakshmikantham D. Trigiante: Theory of Difference Equations.Numerical Methods and Applications, Academic Press, New York, 1988. MR 0939611 |
| Reference:
|
[13] R. Musielak J. Popenda: On periodic solutions of a first order difference equation.Anale Stiintifice Ale Universitatii "Al. I. Cuza" Din Iasi, 34, s. I a, Matematica 2 (1988), 125-133. MR 0995496 |
| Reference:
|
[14] A. Peterson: Boundary value problems for an nth order linear difference equation.SIAM J. Math. Anal. 15 (1984), 124-132. Zbl 0532.39001, MR 0728687, 10.1137/0515008 |
| Reference:
|
[15] A. Peterson: Existence and uniqueness theorems for nonlinear difference equations.J. Math. Anal. Appl. 125 (1987), 185-191. Zbl 0625.39002, MR 0891358, 10.1016/0022-247X(87)90173-9 |
| Reference:
|
[16] Y. Rodriguez: On nonlinear discrete boundary value problems.J. Math. Anal. Appl. 114 (1986), 398-408. Zbl 0681.39002, MR 0833595, 10.1016/0022-247X(86)90092-2 |
| Reference:
|
[17] A. M. Samoilenko: Numerical-analytic method of investigation of systems of ordinary differential equations, I.Ukrain. Math. Journal 17 (1965), 82-93. (In Russian.) MR 0195266 |
| Reference:
|
[18] A. M. Samoilenko: Numerical-analytic method of investigation of systems of ordinary differential equations, II.Ukrain. Math. Journal 18 (1966), 50-59. (In Russian.) MR 0195267 |
| Reference:
|
[19] A. M. Samoilenko N. I. Ronto: A modification of numerical-analytic method of successive approximations for boundary value problems for ordinary differential equations.Ukrain. Math. Journal 42 (1990), 1107-1116. (In Russian.) MR 1078829 |
| Reference:
|
[20] A. M. Samoilenko N. I. Ronto: Numerical-analytic Method of Investigation of Periodic Solutions.Vyssha Shkola Publications, Kiev, 1976. (In Russian.) MR 0508530 |
| Reference:
|
[21] A. M. Samoilenko N. I. Ronto: Numerical-analytic Method of Investigation of Solutions of Boundary value problems.Naukova Dumka Publications, Kiev, 1986. (In Russian.) MR 0886480 |
| . |
