Power series solutions for the $m$th-order-matrix ordinary differential equation
Authors:
Julio Ruiz-Claeyssen and Mauro Zevallos Gutierrez
Journal:
Quart. Appl. Math. 37 (1980), 447-450
MSC:
Primary 34A25; Secondary 34A30
DOI:
https://doi.org/10.1090/qam/564736
MathSciNet review:
564736
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Abstract: A description of the fundamental solution of the mth-order linear ordinary differential equation with matrix coefficients is given in terms of power series and the Green function. The second-order equation is discussed.
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1988. General theory; With the assistance of William G. Bade and Robert G. Bartle; Reprint of the 1958 original; A Wiley-Interscience Publication. MR 1009162
- S. Fenyö, Modern mathematical methods in technology. Vol. 2, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., New York, 1975. Translated from the German; North-Holland Series in Applied Mathematics and Mechanics, Vol. 17. MR 0471491
- Jack K. Hale, Ordinary differential equations, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. Pure and Applied Mathematics, Vol. XXI. MR 0419901
- Ignace I. Kolodner, On exp$(tA)$ with $A$ satisfying a polynomial, J. Math. Anal. Appl. 52 (1975), no. 3, 514–524. MR 425612, DOI https://doi.org/10.1016/0022-247X%2875%2990076-1
- Peter Lancaster, Theory of matrices, Academic Press, New York-London, 1969. MR 0245579
- R. F. Rinehart, The equivalence of definitions of a matric function, Amer. Math. Monthly 62 (1955), 395–414. MR 69908, DOI https://doi.org/10.2307/2306996
- M. Roseau, Équations différentielles, Masson, Paris-New York-Barcelona, 1976 (French). Maîtrise de Mathématiques. MR 0486708
J. Ruiz and M. Zevallos, Fundamental solutions of matrix ordinary differential equations (Fourth Latin-American School of Mathematics, July 1978, Lima)
N. Dunford and J. Schwartz, Linear operators, part I: general theory, John Wiley, 1957
S. Fenyo, Modern mathematical methods in technology, Vol. 2, North-Holland, 1975
J. Hale, Ordinary differential equations, John Wiley, 1969
I. Kolodner, On exp(tA) with A satisfying a polynomial, J. Math. Anal. App. 514–524 (1975)
P. Lancaster, Theory of Matrices, Academic Press, 1969
R. F. Rinehart, The equivalence of definitions of a matrix function, Amer. Math. Monthly, 35, 395–414 (1955)
M. Rosseau, Equations differentielles, Masson S. A., 1976
J. Ruiz and M. Zevallos, Fundamental solutions of matrix ordinary differential equations (Fourth Latin-American School of Mathematics, July 1978, Lima)
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Article copyright:
© Copyright 1980
American Mathematical Society
