Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions

Lucas Jódar

Applications of Mathematics (1994)

  • Volume: 39, Issue: 1, page 1-13
  • ISSN: 0862-7940

Abstract

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In this paper we obtain existence conditions and an explicit closed form expression of the general solution of twopoint boundary value problems for coupled systems of second order differential equations with a singularity of the first kind. The approach is algebraic and is based on a matrix representation of the system as a second order Euler matrix differential equation that avoids the increase of the problem dimension derived from the standard reduction of the order method.

How to cite

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Jódar, Lucas. "Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions." Applications of Mathematics 39.1 (1994): 1-13. <http://eudml.org/doc/32865>.

@article{Jódar1994,
abstract = {In this paper we obtain existence conditions and an explicit closed form expression of the general solution of twopoint boundary value problems for coupled systems of second order differential equations with a singularity of the first kind. The approach is algebraic and is based on a matrix representation of the system as a second order Euler matrix differential equation that avoids the increase of the problem dimension derived from the standard reduction of the order method.},
author = {Jódar, Lucas},
journal = {Applications of Mathematics},
keywords = {Coupled differential system; boundary value problem; singularity of the first kind; Moore-Penrose pseudo-inverse; explicit solutions; Moore-Penrose pseudo-inverse; two point boundary value problems; coupled systems of second order differential equations; singularity; second order Euler matrix differential equation},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions},
url = {http://eudml.org/doc/32865},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Jódar, Lucas
TI - Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 1
SP - 1
EP - 13
AB - In this paper we obtain existence conditions and an explicit closed form expression of the general solution of twopoint boundary value problems for coupled systems of second order differential equations with a singularity of the first kind. The approach is algebraic and is based on a matrix representation of the system as a second order Euler matrix differential equation that avoids the increase of the problem dimension derived from the standard reduction of the order method.
LA - eng
KW - Coupled differential system; boundary value problem; singularity of the first kind; Moore-Penrose pseudo-inverse; explicit solutions; Moore-Penrose pseudo-inverse; two point boundary value problems; coupled systems of second order differential equations; singularity; second order Euler matrix differential equation
UR - http://eudml.org/doc/32865
ER -

References

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  8. MACSYMA, MACSYMA Symbolics Inc., 1989. (1989) Zbl0745.33007
  9. MATLAB user’s guide, Technical Report CS81-1 (1980), Computer Sci. Department, Univ. of New Mexico, Alburquerque. (1980) 
  10. Numerical analysis, a second course, Academic Press, 1972. (1972) Zbl0248.65001MR0403154
  11. Generalized inverse of matrices and its applications, John-Wiley, 1971. (1971) MR0338013
  12. Eine Taylorreihenmethode zur numerischen Lösung von Zwei-Punkt Randwertproblemen mit Anwendung auf singuläre Probleme der nichtlinearen Schalentheorie, TUM, Institut für Mathematik, München, 1977. (1977) 
  13. 10.1137/0515023, SIAM J. Math. Anal. 15 (1984), 287–307. (1984) DOI10.1137/0515023

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