| Title:
|
One-step methods for two-point boundary value problems in ordinary differential equations with parameters (English) |
| Author:
|
Jankowski, Tadeusz |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
81-95 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A general theory of one-step methods for two-point boundary value problems with parameters is developed. On nonuniform nets $h_n$, one-step schemes are considered. Sufficient conditions for convergence and error estimates are given. Linear or quadratic convergence is obtained by Theorem 1 or 2, respectively. (English) |
| Keyword:
|
one-step methods |
| Keyword:
|
two-point boundary value problems |
| MSC:
|
34B15 |
| MSC:
|
65L06 |
| MSC:
|
65L10 |
| idZBL:
|
Zbl 0817.65067 |
| idMR:
|
MR1258185 |
| DOI:
|
10.21136/AM.1994.134246 |
| . |
| Date available:
|
2009-09-22T17:43:05Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134246 |
| . |
| Reference:
|
[1] E.A. Coddington and N. Levinson: Theory of ordinary differentical equations.McGraw-Hill, New York, 1955. MR 0069338 |
| Reference:
|
[2] J.W. Daniel and R.E. Moore: Computation and theory in ordinary differential equations.W.H. Freeman, San Francisco, 1970. MR 0267765 |
| Reference:
|
[3] P. Henrici: Discrete variable methods in ordinary differential equations.John Wiley, New York, 1962. Zbl 0112.34901, MR 0135729 |
| Reference:
|
[4] T. Jankowski: Boundary value problems with a parameter of differentical equations with deviated arguments.Math. Nachr. 125 (1986), 7-28. MR 0847349, 10.1002/mana.19861250103 |
| Reference:
|
[5] T. Jankowski: One-step methods for ordinary differential equations with parameters.Apl. Mat. 35 (1990), 67-83. Zbl 0701.65053, MR 1039412 |
| Reference:
|
[6] T. Jankowski: On the convergence of multistep methods for nonlinear two-point boundary value problems.APM (1991), 185–200. Zbl 0746.65060, MR 1109587 |
| Reference:
|
[7] H.B. Keller: Numerical methods for two point boundary value problems.Waltham, Blaisdell, 1968. Zbl 0172.19503, MR 0230476 |
| Reference:
|
[8] H.B. Keller: Numerical solution of two-point boundary value problems.Society for Industrial and Applied Mathematics, Philadelphia 24, 1976. MR 0433897 |
| Reference:
|
[9] A. Pasquali: Un procedimento di calcolo connesso ad un noto problema ai limiti per l’equazione $\dot{x}=f(t,x,\lambda )$.Mathematiche 23 (1968), 319-328. MR 0267785 |
| Reference:
|
[10] T. Pomentale: A constructive theorem of existence and uniqueness for the problem $y^{\prime }=f(x,y,\lambda ), y(a)=\alpha , y(b)=\beta $.ZAMM 56 (1976), 387-388. Zbl 0338.34019, MR 0430389, 10.1002/zamm.19760560806 |
| Reference:
|
[11] Z.B. Seidov: A multipoint boundary value problem with a parameter for systems of differential equations in Banach space.Sibirski Math. Z. 9 (1968), 223-228. (Russian) MR 0281987 |
| Reference:
|
[12] J. Stoer and R. Bulirsch: Introduction to numerical analysis.Springer-Verlag, New York, 1980. MR 0557543 |
| . |
