ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 34B15 Rontó, Miklós, University of Miskolc, Hungary A numerical-analytic method for parametrized BVPs The following non-linear two-point boundary value problem (BVP) containing parameters both in the differential equation and the boundary condition is considered: \frac{dx}{dt} = f(t, x, λ_{1}), Ax(0) + C(λ_{1})x(λ_{2}) = d(λ_{1}, λ_{2}), x_{1}(0) = x_{10}, x_{2}(0) = x_{20}. Here f : [0, T] × D × [a, b] → ℝ^{n}, D ⊂ ℝ^{n}, d : [a, b] × [0, T] → ℝ^{n}, det C(λ_{1}) ≠ 0; λ_{1} ∈ [a, b] and λ_{2} ∈ [0, T] are unknown scalar parameters. We give a numerical-analytic successive approximation method to establish existence theorems for a solution (x^{∗}, λ_{1}^{∗}, λ_{2}^{∗}) as well as to construct approximations to this solution. A survey of investigations concerning the method under consideration for various types of BVPs can be found in [1, 2]. References: [1] A. M. Samoilenko and N. I. Ronto, Numerical-analytic Methods of Investigating Periodic Solutions, Mir Publishers, Moscow, 1979. [2] A. M. Samoilenko and N. I. Ronto, Numerical-analytic Methods in the Theory of Boundary Value Problems, Naukova Dumka, Kiev, 1992 (in Russian).