Abstract
We construct and study exact and truncated self-adjoint three-point variational schemes of any degree of accuracy for self-adjoint eigenvalue problems for systems of second-order ordinary differential equations.
Similar content being viewed by others
References
I. L. Makarov, “Variational-difference schemes of high degree of accuracy for the Sturm-Liouville problem,”Dokl Akad. NaukUkr. SSR, Ser. A, No. 2, 30–32 (1987).
V. G. Prikazchikov, “Homogeneous difference schemes and schemes of high degree of accuracy for the Sturm-Liouville problem,”Zh. Vych. Mat. Mat. Fiz.,9, No. 2, 315–336 (1969).
I. L. Makarov, “Exact and truncated difference schemes for vector Sturm-Liouville problem,”Vych. Prikl Matematika, Issue 49, 72–84 (1983).
I. L. Makarov, V. L. Makarov, and V. G. Prikazchikov, “Exact difference schemes of arbitrary degree of accuracy for systems of second-orderdifferential equations,”Differents. Uravn.,15, No. 7, 1194–1205 (1979).
I. L. Makarov, “Self-adjoint difference schemes of arbitrary degree of accuracy for second-order vector boundary-value problems,”in:Application of Mathematical Methods and Computers in Control and Design Systems [in Russian], Institute of Cybernetics, Ukrainian Academy of Sciences, Kiev (1991), pp. 19–29.
G. Strang and G. J. Fix,An Analysis of the Finite Element Method [Russian translation], Mir, Moscow 1977.
U. Mertins, “Zur Konvergenz des Rayleigh-Ritz-Verfahrens bei Eigenwertaufgaben,”Numer. Math.,59, 667–682 (1991).
Rights and permissions
About this article
Cite this article
Makarov, I.L. Variational schemes for vector eigenvalue problems. Ukr Math J 48, 1708–1716 (1996). https://doi.org/10.1007/BF02529492
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02529492