Geodesic
Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions
Applications of Mathematics, Tome 39 (1994) no. 1, pp. 1-13
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.21136/AM.1994.134239
Classification : 34A05, 34B05
Keywords: Coupled differential system; boundary value problem; singularity of the first kind; Moore-Penrose pseudo-inverse 
@article{10_21136_AM_1994_134239,
     author = {J\'odar, Lucas},
     title = {Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions},
     journal = {Applications of Mathematics},
     pages = {1--13},
     year = {1994},
     volume = {39},
     number = {1},
     doi = {10.21136/AM.1994.134239},
     mrnumber = {1254743},
     zbl = {0795.34011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134239/}
}
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
SP  - 1
EP  - 13
VL  - 39
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134239/
DO  - 10.21136/AM.1994.134239
LA  - en
ID  - 10_21136_AM_1994_134239
ER  - 
%0 Journal Article
%A Jódar, Lucas
%T Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions
%J Applications of Mathematics
%D 1994
%P 1-13
%V 39
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1994.134239/
%R 10.21136/AM.1994.134239
%G en
%F 10_21136_AM_1994_134239
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, Tome 39 (1994) no. 1, pp. 1-13. doi: 10.21136/AM.1994.134239

[1] S. L. Campbell and C. D. Meyer, jr.: Generalized inverses of linear transformations. Pitman Pubs. Co., 1979.

[2] I. S. Gradshteyn and I. M. Ryzhik: Table of integrals, series and products. Academic Press, 1980. | MR

[3] L. Jódar: Boundary value problems and Cauchy problems for the second order Euler operator differential equation. Linear Algebra Appls. 91 (1987), 1–12. | MR

[4] L. Jódar: Explicit solutions of two-point boundary value problems. Math. Zeitschrift 199 (1988), 555–564. | DOI | MR

[5] L. Jódar: On the Euler differential equation $A_2 t^2 X^{\prime \prime }+tA_1 X^{\prime }+A_0 X=0$. Applied Maths. Letters 2(3) (1989), 233–237. | MR

[6] H. B. Keller and A. W. Wolfe: On the nonunique equilibrium states and buckling mechanism of spherical shells. J. Soc. Indust. Applied Maths. 13 (1965), 674–705. | DOI | MR

[7] P. Lancaster and M. Tismenetsky: The theory of matrices. Academic Press, second ed., 1985. | MR

[8] MACSYMA. MACSYMA Symbolics Inc., 1989. | Zbl

[9] C. B. Moler: MATLAB user’s guide. Technical Report CS81-1 (1980), Computer Sci. Department, Univ. of New Mexico, Alburquerque.

[10] J. M. Ortega: Numerical analysis, a second course. Academic Press, 1972. | MR | Zbl

[11] C. R. Rao and S. K. Mitra: Generalized inverse of matrices and its applications. John-Wiley, 1971. | MR

[12] P. Rentrop: Eine Taylorreihenmethode zur numerischen Lösung von Zwei-Punkt Randwertproblemen mit Anwendung auf singuläre Probleme der nichtlinearen Schalentheorie. TUM, Institut für Mathematik, München, 1977.

[13] E. Weinmüller: On the boundary value problem for systems of ordinary second order differential equations with a singularity of the first kind. SIAM J. Math. Anal. 15 (1984), 287–307. | DOI

Cité par Sources :