Solutions to linear matrix ordinary differential equations via minimal, regular, and excessive space extension based universalization

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 polynomially varying with the independent variable. Work aims to get a universal form for this equation by using the space extension concept where new unknowns are defined to get more amenable form for the equation. The convergence of the series solution to this equation obtained via minimal, regular, and excessive space extension is also investigated with the aid of an appropriate norm analysis which also enables us to get error estimates for the truncated series solutions. A few illustrative examples are presented for practical convergence issues like approximation quality.