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Keywords:
one-step methods; two-point boundary value problems
one-step methods; two-point boundary value problems
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.
References:
[1] E.A. Coddington and N. Levinson: Theory of ordinary differentical equations. McGraw-Hill, New York, 1955. MR 0069338
[2] J.W. Daniel and R.E. Moore: Computation and theory in ordinary differential equations. W.H. Freeman, San Francisco, 1970. MR 0267765
[3] P. Henrici: Discrete variable methods in ordinary differential equations. John Wiley, New York, 1962. MR 0135729 | Zbl 0112.34901
[4] T. Jankowski: Boundary value problems with a parameter of differentical equations with deviated arguments. Math. Nachr. 125 (1986), 7-28. DOI 10.1002/mana.19861250103 | MR 0847349
[5] T. Jankowski: One-step methods for ordinary differential equations with parameters. Apl. Mat. 35 (1990), 67-83. MR 1039412 | Zbl 0701.65053
[6] T. Jankowski: On the convergence of multistep methods for nonlinear two-point boundary value problems. APM (1991), 185–200. MR 1109587 | Zbl 0746.65060
[7] H.B. Keller: Numerical methods for two point boundary value problems. Waltham, Blaisdell, 1968. MR 0230476 | Zbl 0172.19503
[8] H.B. Keller: Numerical solution of two-point boundary value problems. Society for Industrial and Applied Mathematics, Philadelphia 24, 1976. MR 0433897
[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
[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 10.1002/zamm.19760560806 | MR 0430389 | Zbl 0338.34019
[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
[12] J. Stoer and R. Bulirsch: Introduction to numerical analysis. Springer-Verlag, New York, 1980. MR 0557543
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