Numerical approximations of second-order matrix differential equations using higher degree splines

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 non-stiff initial problems using higher degree matrix splines without any dimensional increase. An estimation of the approximation error for some illustrative examples are presented by using Mathematica. Several MatLab functions have also been developed, comparing, under equal conditions, accuracy and execution times with built-in MatLab functions. Experimental results show the advantages of solving the above initial problem by using the implemented MatLab functions.

Keywords:

• matrix models
• second-order matrix differential equations
• matrix splines
• approximations for non-stiff initial problems
• extended MatLab functions

AMS Subject Classifications:

• 15A99
• 65D07
• 65F30
• 65Y04
• 34L99

Acknowledgements

We also appreciate the valuable comments made by the anonymous referee to improve the original manuscript.

Notes

The authors wish to thank for financial support by the Universidad Politécnica de Valencia [grant number PAID-06-11-2020]