Dynamic solutions of linear matrix differential equations
Authors:
Julio Cesar Ruiz-Claeyssen and Teresa Tsukazan
Journal:
Quart. Appl. Math. 48 (1990), 169-179
MSC:
Primary 34A30; Secondary 65L05
DOI:
https://doi.org/10.1090/qam/1040240
MathSciNet review:
MR1040240
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Abstract: We discuss the $m$th-order linear differential equation with matrix coefficients in terms of a particular matrix solution that enjoys properties similar to the exponential of first-order equations. A new formula for the exponential matrix is established with dynamical solutions related to the generalized Lucas polynomials.
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J. Ruiz-Claeyssen, A variation of constants formula with the dynamical solution of matrix differential equations, Tech. Rep. No. 2, UFRGS, Porto Alegre, 1985
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H. Schwerdtfeger, Les fonctions de matrices, Hermann Editeurs, Paris, 1938
R. Bakarat and E. Baumann, Mth power of an $N \times N$ matrix and its connection with the generalized Lucas polynomials, J. Math. Phys. 10, (1969)
J. Bartak, Stability and correctness of abstract differential equations in Hilbert spaces, Czech Math. J 28 (103), 1978
M. Bruschi and P. E. Ricci, An explicit formula for f(A) and the generalized Lucas polynomials, SIAM J. Math. Anal. 13, (1982)
D. Gottlieb and S. Orzsag, Numerical Analysis of Spectral Methods, SIAM Regional Series, 1977
J. Hale, Ordinary Differential Equations, John Wiley, 1969
P. Lancaster and M. Tismenetsky, The Theory of Matrices, Academic Press, Toronto, 1985
J. Lappo-Danilevskiǐ, Théorie des Systèmes des Équations Differentielles Linéaires, Chelsea Publ., 1953
J. La Salle, Stability Theory for Difference Equations, SIAM Regional Conferences Series in Mathematics, 1976
J. L. Lavoie, The mth power of an n x m matrix and the Bell polynomials, SIAM J. App. Math. 29 (3), (1975)
C. Moler and Ch. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, SIAM Rev 20, (1978)
J. Ruiz-Claeyssen and M. Zevallos, Power series solutions for the mth-order matrix differential equation, Quart. Appl. Math. 47, (1980)
J. Ruiz-Claeyssen, M. Davila, and T. Tsukazan, Factor block circulants and even order undamped matrix differential equations, Mat. Apl. Comput. 2 (1), (1983)
J. Ruiz-Claeyssen, A variation of constants formula with the dynamical solution of matrix differential equations, Tech. Rep. No. 2, UFRGS, Porto Alegre, 1985
Hans-J. Runckel and U. Pittelkow, Practical Computation of Matrix Functions, Linear Algebra App. 49,(1983)
H. Schwerdtfeger, Les fonctions de matrices, Hermann Editeurs, Paris, 1938
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Article copyright:
© Copyright 1990
American Mathematical Society
