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

Volume 22 / 1993

Enrique Navarro, Rafael Company, Lucas Jódar Applicationes Mathematicae 22 (1993), 11-23 DOI: 10.4064/am-22-1-11-23

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.

Authors

  • Enrique Navarro
  • Rafael Company
  • Lucas Jódar

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