Geodesic
One-step methods for two-point boundary value problems in ordinary differential equations with parameters
Applications of Mathematics, Tome 39 (1994) no. 2, pp. 81-95

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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.
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.
DOI : 10.21136/AM.1994.134246
Classification : 34B15, 65L06, 65L10
Keywords: one-step methods; two-point boundary value problems 
Jankowski, Tadeusz. One-step methods for two-point boundary value problems in ordinary differential equations with parameters. Applications of Mathematics, Tome 39 (1994) no. 2, pp. 81-95. doi: 10.21136/AM.1994.134246
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[1] E.A. Coddington and N. Levinson: Theory of ordinary differentical equations. McGraw-Hill, New York, 1955. | MR

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

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

[4] T. Jankowski: Boundary value problems with a parameter of differentical equations with deviated arguments. Math. Nachr. 125 (1986), 7-28. | DOI | MR

[5] T. Jankowski: One-step methods for ordinary differential equations with parameters. Apl. Mat. 35 (1990), 67-83. | MR | Zbl

[6] T. Jankowski: On the convergence of multistep methods for nonlinear two-point boundary value problems. APM (1991), 185–200. | MR | Zbl

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

[8] H.B. Keller: Numerical solution of two-point boundary value problems. Society for Industrial and Applied Mathematics, Philadelphia 24, 1976. | MR

[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

[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. | DOI | MR | Zbl

[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

[12] J. Stoer and R. Bulirsch: Introduction to numerical analysis. Springer-Verlag, New York, 1980. | MR

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