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POWER SERIES SOLUTIONS OF SINGULAR LINEAR SYSTEMS

JEN-YIN HAN

Mathematics Branch, Nei-Li High School, Nei-Li 320, Tao-Yuan County, Taiwan

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and

CHIN-YUAN LIN

Department of Mathematics, National Central University, Chung-Li 320, Taiwan

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https://doi.org/10.1142/S0129167X12500346Cited by:0 (Source: Crossref)

Abstract

By using exponential functions, a fundamental set of power series solutions for singular linear systems of the first kind is explicitly computed.

Keywords:

AMSC: 15A21, 34A30

References

T. M. Apostol , Mathematical Analysis ( Addision-Wesley Publishing Company , 1974 ) . Google Scholar
W. Balser , Formal Power Series and Linear Systems of Meromorphic Ordinary Differential Equations ( Springer-Verlag , New York , 2000 ) . Google Scholar
E. A. Coddington , Introduction to Ordinary Differential Equations ( Prentice-Hall , Englewood Cliffs, New Jersey , 1961 ) . Google Scholar
E. A. Coddington and N. Levision , Theory of Ordinary Differential Equations ( McGraw-Hill Book Company , New York , 1955 ) . Google Scholar
C. G. Cullen , Matrices and Linear Transforms , 2nd edn. ( Dover Publications , New York , 1972 ) . Google Scholar
C. G. Cullen , Linear Algebra and Differential Equations , 2nd edn. ( PWS-KENT Publishing Company , Boston, Massachussetts , 1991 ) . Google Scholar
P. Davies and N. J. Higham, SIAM J. Matrix Anal. Appl. 25(2), 464 (2003), DOI: 10.1137/S0895479802410815. Crossref, Web of Science, Google Scholar
S. H. Friedberg , A. J. Insel and L. E. Spence , Linear Algebra , 2nd edn. ( Prentice-Hall , New Jersey , 1989 ) . Google Scholar
F. R. Gantmacher , The Theory of Matrices I ( Chelsea , New York , 1959 ) . Google Scholar
F. R. Gantmacher , The Theory of Matrices II ( Chelsea , New York , 1959 ) . Google Scholar
J.-Y. Han and C.-Y. Lin, Linear Multilinear Algebra 57(4), 369 (2009), DOI: 10.1080/03081080701799437. Crossref, Web of Science, Google Scholar
Ph. Hartman , Ordinary Differential Equations ( John Wiley and Sons , New York , 1964 ) . Google Scholar
N. J. Higham, SIAM J. Matrix Anal. Appl. 26, 1179 (2005), DOI: 10.1137/04061101X. Crossref, Web of Science, Google Scholar
K. Hoffman and R. Kunze , Linear Algebra , 2nd edn. ( Prentice-Hall , Englewood Cliffs, NJ , 1971 ) . Google Scholar
R. A. Horn and C. R. Johnson , Matrix Analysis ( Cambridge University Press , New York , 1988 ) . Google Scholar
P. Lancaster and M. Tismenetsky , The Theory of Matrices with Applications , 2nd edn. ( Academic Press , New York , 1985 ) . Google Scholar
C.-Y. Lin , Theory and Examples of Ordinary Differential Equations ( World Scientific , Singapore , 2011 ) . Link, Google Scholar
C. Moler and C. Van Loan, SIAM Rev. 45, 3 (2003), DOI: 10.1137/S00361445024180. Crossref, Web of Science, Google Scholar
R. K. Nagel and E. B. Saff , Fundamentals of Differential Equations and Boundary Value Problems , 2nd edn. ( Addison-Wesley Publishing Company , New York , 1996 ) . Google Scholar
A. E. Taylor and D. Lay , Introduction to Functional Analysis ( Wiley , 1980 ) . Google Scholar
W. Walter , Ordinary Differential Equations ( Springer-Verlag , New York , 1998 ) . Crossref, Google Scholar