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

Authors:
M. M. Tung;E. Defez;J. Sastre
Affiliations:
Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n, E-46022 Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n, E-46022 Valencia, Spain;Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universidad Politécnica de Valencia, Camino de Vera, s/n, E-46022 Valencia, Spain
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

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.