| Title:
|
Boundary value problems for the mildly non-linear ordinary differential equation of the fourth order (English) |
| Author:
|
Růžičková, Helena |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
19 |
| Issue:
|
4 |
| Year:
|
1974 |
| Pages:
|
216-231 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the finite difference method is applied to a boundary value problem for the mildly non-linear ordinary differential equation of the fourth order. The existence of a unique solution of both the differential and the difference problem is proved and an $O(h^2)$ estimate of the discretization error and its first difference quotient is derived. Some numerical examples are given. () |
| MSC:
|
34B15 |
| MSC:
|
65J99 |
| MSC:
|
65L10 |
| idZBL:
|
Zbl 0317.34012 |
| idMR:
|
MR0346235 |
| DOI:
|
10.21136/AM.1974.103536 |
| . |
| Date available:
|
2008-05-20T17:59:09Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103536 |
| . |
| Reference:
|
[1] Babuška I., Práger M., Vitásek E.: Numerical Processes in Differential Equations.Publishers of Technical Literature, Prague and Interscience Publishers, a Division of John Wiley & Sons, London - New York - Sydney 1966. MR 0223101 |
| Reference:
|
[2] Gary J.: Computing Eigenvalues of Ordinary Differential Equations by Finite Differences.Mathematics of Computation, 19, No 91, (1965), p. 365-379. MR 0179926, 10.1090/S0025-5718-1965-0179926-X |
| Reference:
|
[3] Хао-Шоу: Однородные разностные схемы для уравнения четвертого порядка с разрывными коэффициентами.Ж. вычисл. матем. и матем. физ., 3, № 5, (1963), р. 841-860. Zbl 1145.93303, MR 0157491 |
| Reference:
|
[4] Lees M.: Discrete Methods for Nonlinear two-point Boundary Value Problems.Numerical Solution of Partial Differential Equations, (J. H. Bramble, editor), p. 59-72, New York, Academic Press, 1966. Zbl 0148.39206, MR 0202323 |
| Reference:
|
[5] Marek I.: On Approximate Methods in Eigenvalue Problems.Čas. pro pěst. mat., 92 (1967), p. 89-104. Zbl 0167.13903, MR 0211598 |
| Reference:
|
[6] Růžičková H.: Boundary Value Problems for Ordinary Differential Equations of the 4th Order.(Czech). (Unpublished), CSc Thesis, VUT Brno, 1971. |
| Reference:
|
[7] Самарский А. А.: Априорные оценки для разностных уравнений.Ж. вычисл, матем. и мат. физ., 1, № 6, (1961), р. 972-1000. Zbl 1160.68305, MR 0148238 |
| Reference:
|
[8] Zlámal M.: On Mildly Nonlinear Elliptic Boundary Value Problems.Information Processing 68, p. 179-182, North-Holland Publ. Соmр. - Amsterdam 1969. MR 0258296 |
| Reference:
|
[9] Zlámal M.: Discretization and Error Estimates for Boundary Value Problems of the Second Order.Estrato da Calcolo, Vol. 4, fasc. 3, (1967), p. 541 - 550. MR 0275691, 10.1007/BF02576039 |
| . |
