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

Enrique Navarro; Rafael Company; Lucas Jódar

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 11-23
  • ISSN: 1233-7234

Abstract

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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 × n complex matrix and X(t) is an n × 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.

How to cite

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Navarro, Enrique, Company, Rafael, and Jódar, Lucas. "Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems." Applicationes Mathematicae 22.1 (1993): 11-23. <http://eudml.org/doc/219076>.

@article{Navarro1993,
abstract = {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.},
author = {Navarro, Enrique, Company, Rafael, Jódar, Lucas},
journal = {Applicationes Mathematicae},
keywords = {initial value problem; closed form solution; fundamental set; boundary value problem; Bessel matrix equation; general solution; coupled system of Bessel differential equations; linear differential equations; series solutions; two-point boundary-value problem},
language = {eng},
number = {1},
pages = {11-23},
title = {Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems},
url = {http://eudml.org/doc/219076},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Navarro, Enrique
AU - Company, Rafael
AU - Jódar, Lucas
TI - Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 11
EP - 23
AB - 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.
LA - eng
KW - initial value problem; closed form solution; fundamental set; boundary value problem; Bessel matrix equation; general solution; coupled system of Bessel differential equations; linear differential equations; series solutions; two-point boundary-value problem
UR - http://eudml.org/doc/219076
ER -

References

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  10. [9] J. M. Ortega, Numerical Analysis. A Second Course, Academic Press, New York, 1972 Zbl0248.65001
  11. [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 Zbl0331.65052
  12. [11] C. R. Rao and S. K. Mitra, Generalized Inverses of Matrices and its Applications, Wiley, New York, 1971 Zbl0236.15004
  13. [12] M. Rosenblum, On the operator equation BX - XA = Q, Duke Math. J. 23 (1956), 263-269. 
  14. [13] E. Weinmüller, A difference method for a singular boundary value problem of second order, Math. Comp. 42 (166) (1984), 441-464 Zbl0573.65063

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