# 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

## Access Full Article

top## Abstract

top## How to cite

topNavarro, 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

top- [1] S. L. Campbell and C. D. Meyer Jr., Generalized Inverses of Linear Transformations, Pitman, London, 1979 Zbl0417.15002
- [2] C. Davis and P. Rosenthal, Solving linear operator equations, Canad. J. Math. 26 (6) (1974), 1384-1389 Zbl0297.47011
- [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 Zbl0595.34022
- [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 Zbl0148.19801
- [9] J. M. Ortega, Numerical Analysis. A Second Course, Academic Press, New York, 1972 Zbl0248.65001
- [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
- [11] C. R. Rao and S. K. Mitra, Generalized Inverses of Matrices and its Applications, Wiley, New York, 1971 Zbl0236.15004
- [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 Zbl0573.65063

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.