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1993-1995 | 22 | 1 | 11-23
Tytuł artykułu

Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems

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EN
Abstrakty
EN
In this paper we consider Bessel equations of the type $t^2 X^{(2)}(t) + t X^{(1)}(t) + (t^2 I - A^2)X(t) = 0$, where A is an n$\times$n complex matrix and X(t) is an n$\times$m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
Rocznik
Tom
22
Numer
1
Strony
11-23
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-3-21
Twórcy
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22.012, 46022 Valencia, Spain
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22.012, 46022 Valencia, Spain
autor
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22.012, 46022 Valencia, Spain
Bibliografia
  • [1] S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Pitman, London, 1979
  • [2] C. Davis and P. Rosenthal, Solving linear operator equations, Canad. J. Math. 26 (6) (1974), 1384-1389
  • [3] N. Dunford and J. Schwartz, Linear Operators, Part I, Interscience, New York, 1957
  • [4] E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, 1969
  • [5] L. Jódar, Explicit expressions for Sturm-Liouville operator problems, Proc. Edinburgh Math
  • [Soc] 30 (1987), 301-309
  • [6] 30 (1987), Explicit solutions for second order operator differential equations with two boundary value conditions, Linear Algebra Appl. 103 (1988), 35-53
  • [7] T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, N.J., 1980
  • [8] H. B. Keller and A. W. Wolfe, On the nonunique equilibrium states and buckling mechanism of spherical shells, J. Soc. Indust. Appl. Math. 13 (1965), 674-705
  • [9] J. M. Ortega, Numerical Analysis. A Second Course, Academic Press, New York, 1972
  • [10] S. V. Parter, M. L. Stein and P. R. Stein, On the multiplicity of solutions of a differential equation arising in chemical reactor theory, Tech. Rep. 194, Dept. of Computer Sciences, Univ. of Wisconsin, Madison, 1973
  • [11] C. R. Rao and S. K. Mitra, Generalized Inverses of Matrices and its Applications, Wiley, New York, 1971
  • [12] M. Rosenblum, On the operator equation BX - XA = Q, Duke Math. J. 23 (1956), 263-269.
  • [13] E. Weinmüller, A difference method for a singular boundary value problem of second order, Math. Comp. 42 (166) (1984), 441-464
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