| Title:
|
Boundary value problems for coupled systems of second order differential equations with a singularity of the first kind: explicit solutions (English) |
| Author:
|
Jódar, Lucas |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1994 |
| Pages:
|
1-13 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Coupled differential system |
| Keyword:
|
boundary value problem |
| Keyword:
|
singularity of the first kind |
| Keyword:
|
Moore-Penrose pseudo-inverse |
| MSC:
|
34A05 |
| MSC:
|
34B05 |
| idZBL:
|
Zbl 0795.34011 |
| idMR:
|
MR1254743 |
| DOI:
|
10.21136/AM.1994.134239 |
| . |
| Date available:
|
2009-09-22T17:42:21Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134239 |
| . |
| Reference:
|
[1] S. L. Campbell and C. D. Meyer, jr.: Generalized inverses of linear transformations.Pitman Pubs. Co., 1979. |
| Reference:
|
[2] I. S. Gradshteyn and I. M. Ryzhik: Table of integrals, series and products.Academic Press, 1980. MR 1773820 |
| Reference:
|
[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 0888475 |
| Reference:
|
[4] L. Jódar: Explicit solutions of two-point boundary value problems.Math. Zeitschrift 199 (1988), 555–564. MR 0968321, 10.1007/BF01161644 |
| Reference:
|
[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 1013885 |
| Reference:
|
[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. MR 0183174, 10.1137/0113045 |
| Reference:
|
[7] P. Lancaster and M. Tismenetsky: The theory of matrices.Academic Press, second ed., 1985. MR 0792300 |
| Reference:
|
[8] : MACSYMA.MACSYMA Symbolics Inc., 1989. Zbl 0745.33007 |
| Reference:
|
[9] C. B. Moler: MATLAB user’s guide.Technical Report CS81-1 (1980), Computer Sci. Department, Univ. of New Mexico, Alburquerque. |
| Reference:
|
[10] J. M. Ortega: Numerical analysis, a second course.Academic Press, 1972. Zbl 0248.65001, MR 0403154 |
| Reference:
|
[11] C. R. Rao and S. K. Mitra: Generalized inverse of matrices and its applications.John-Wiley, 1971. MR 0338013 |
| Reference:
|
[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. |
| Reference:
|
[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. 10.1137/0515023 |
| . |
