Autors: Karandzhulov, L. I., Stoyanova, Y. P.
Title: Boundary value problem for singularly perturbed systems
Keywords: singularly perturbed systems, almost nonlinear system, bound

Abstract: A boundary value problem for almost nonlinear singularly perturbed systems of ordinary differential equations is considered. An asymptotic solution is constructed utilizing boundary functions method and generalized inverse matrices and orthoprojectors.

References

  1. A.A. Boichuk, V.F. Zhjuravliev, A.M. Samoilenko, 1995, Generalized inverse operators and Noether's boundary value problems, Kiev, IM NAN Ukraina
  2. L.I. Karandjulov, 1997, Asymptotic solution of definite class of singularly perturbed linear boundary value problem for ODE, Annuaire Univ. Sofia Fac. Math. Inform., Volume 91(1), pp. 79-95
  3. L.I. Karandjulov, A.A. Boichuk,V.A. Bozhko, 1994, Asymptotic expansion of solution of singularly perturbed linear boundary problems, Dokl. Akad., Nauk Ukraina, Volume 1, pp. 7-10
  4. Penrose R., 1956, On best approximate solution on linear matrix equations, Proc. Cambridge Philos. Soc., Volume 52, pp. 17-19
  5. Penrose R., 1955, A generalize inverse for matrices, Proc. Cambridge Philos. Soc., Volume 51, pp. 406-413
  6. Tikhonov A.N., 1950, On dependence of the solution of differentia equations on small parameter, Mat. sb., Volume 22(2), pp. 193-204
  7. Tikhonov A.N, 1952, System of differential equations with small parameter of the derivatives, Mat. sb., Volume 31(3), pp. 536-575
  8. Vasil'eva A.B., Butuzov V.F., 1950, Asymptotic expansions of solution of singularly perturbed equations, Moscow, Nauka
  9. Wasow W., 1978, Asymptotic expansions for ordinary differential equation, Moscow, Mir

Issue

Boundary value problem for singularly perturbed systems, Applications of Mathematics in Engineering and Economics, Proceedings of the 29-th Summer School, June 2003, Sozopol, pp. 120 – 127, 2004, Bulgaria, Bulvest 2000, ISBN 954-18-0329-6

Вид: публикация в международен форум