Geodesic
One-step methods for ordinary differential equations with parameters
Applications of Mathematics, Tome 35 (1990) no. 1, pp. 67-83
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.
In the present paper we are concerned with the problem of numerical solution of ordinary differential equations with parameters. Our method is based on a one-step procedure for IDEs combined with an iterative process. Simple sufficient conditions for the convergence of this method are obtained. Estimations of errors and some numerical examples are given.
DOI : 10.21136/AM.1990.104388
Classification : 34B15, 65L06, 65L10, 65L15, 65L70
Keywords: ordinary differential equations with parameters; numerical solution; one-step method; parameter estimation; iterative methods; convergence; error estimates; numerical examples 
@article{10_21136_AM_1990_104388,
     author = {Jankowski, Tadeusz},
     title = {One-step methods for ordinary differential equations with parameters},
     journal = {Applications of Mathematics},
     pages = {67--83},
     year = {1990},
     volume = {35},
     number = {1},
     doi = {10.21136/AM.1990.104388},
     mrnumber = {1039412},
     zbl = {0701.65053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104388/}
}
TY  - JOUR
AU  - Jankowski, Tadeusz
TI  - One-step methods for ordinary differential equations with parameters
JO  - Applications of Mathematics
PY  - 1990
SP  - 67
EP  - 83
VL  - 35
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104388/
DO  - 10.21136/AM.1990.104388
LA  - en
ID  - 10_21136_AM_1990_104388
ER  - 
%0 Journal Article
%A Jankowski, Tadeusz
%T One-step methods for ordinary differential equations with parameters
%J Applications of Mathematics
%D 1990
%P 67-83
%V 35
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1990.104388/
%R 10.21136/AM.1990.104388
%G en
%F 10_21136_AM_1990_104388
Jankowski, Tadeusz. One-step methods for ordinary differential equations with parameters. Applications of Mathematics, Tome 35 (1990) no. 1, pp. 67-83. doi: 10.21136/AM.1990.104388

[1] I. Babuška M. Práger E. Vitásek: Numerical processes in differential equations. Praha 1966. | MR

[2] R. Conti: Problemes lineaires pour les équations differentialles ordinaires. Math. Nachr. 23 (1961), 161-178. | DOI | MR

[3] J. W. Daniel R. E. Moore: Computation and theory in ordinary differential equations. San Francisco 1970. | MR

[4] A. Gasparini A. Mangini: Sul calcolo numerico delle soluzioni di un noto problema ai limiti per l'equazione $y' = \lambda f(x,y)$. Le Matematiche 22 (1965), 101-121. | MR

[5] P. Henrici: Discrete variable methods in ordinary differential equations. John Wiley, New York 1962. | MR | Zbl

[6] T. Jankowski M. Kwapisz: On the existence and uniqueness of solutions of boundary-value problem for differential equations with parameter. Math. Nachr. 71 (1976), 237-247. | DOI | MR

[7] H. B. Keller: Numerical methods for two-point boundary-value problems. Blaisdell, London 1968. | MR | Zbl

[8] A. V. Kibenko A. I. Perov: A two-point boundary value problem with parameter. (Russian), Azerbaidzan. Gos. Univ. Učen. Zap. Ser. Fiz.-Mat. i Him. Nauka 3 (1961), 21 - 30. | MR

[9] J. Lambert: Computational methods in ordinary differential equations. London 1973. | MR | Zbl

[10] A. Pasquali: Un procedimento di calcolo connesso ad un noto problema ai limiti per l'equazione $x'=f(t,x,\lambda)$. Le Matematiche 23 (1968), 319-328. | MR | Zbl

[11] Z. B. Seidov: A multipoint boundary value problem with a parameter for systems of differential equations in Banach space. (Russian). Sibirski Math. Z. 9 (1968), 223 - 228. | MR

[12] J. Stoer R. Bulirsch: Introduction to numerical analysis. New York, Heidelberg, Berlin 1980. | MR

[13] H. J. Stetter: Analysis of discretization methods for ordinary differential equations. New York, Heidelberg, Berlin 1973. | MR | Zbl

[14] K. Zawischa: Über die Differentialgleichung $y' = kf(x,y)$ deren Lösungskurve durch zwei gegebene Punkte hindurchgehen soll. Monatsh. Math. Phys. 37 (1930), 103-124. | DOI | MR

Cité par Sources :