Abstract
This work focuses on the solution of the linear matrix ordinary differential equations where the first derivative of the unknown matrix is equal to the same unknown matrix premultiplied by a given matrix polynomial of the independent variable as done in the previous paper. However, this time, not series but perturbation expansions are considered. Sufficient attention is given on the convergence and error estimate issues. The repetitious usage of the perturbation truncations on different but neighbor intervals permits us to define and use so-called “Perturbative Matrix Splines”. This is somehow an analytic continuation issue. Certain illustrative applications are also presented to support the ideas of the work.
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Üsküplü Altınbaşak, S., Demiralp, M. Solutions to linear matrix ordinary differential equations via minimal, regular, and excessive space extension based universalization. J Math Chem 48, 253–265 (2010). https://doi.org/10.1007/s10910-010-9665-7
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DOI: https://doi.org/10.1007/s10910-010-9665-7