Numerical solutions of second-order matrix models using cubic-matrix splines

Many studies of mechanical systems in engineering are based on second-order matrix models. This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for the initial problem Y ″ ( x ) = f ( x , Y (...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2008-11, Vol.56 (10), p.2561-2571
Main Authors: Tung, M.M., Defez, E., Sastre, J.
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computer simulation
Continuous matrix solutions
Cubic splines
Dealing
Differential equations
Mathematical analysis
Mathematical models
Matrix approximations
Matrix models
Second-order matrix differential equations
Splines
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Summary:Many studies of mechanical systems in engineering are based on second-order matrix models. This work discusses the second-order generalization of previous research on matrix differential equations dealing with the construction of approximate solutions for the initial problem Y ″ ( x ) = f ( x , Y ( x ) , Y ′ ( x ) ) using matrix-cubic splines without any dimensional increase. An estimation of the approximation error, the corresponding algorithm of our approach and some illustrative examples are presented.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2008.05.022