Searching for Laurent Solutions of Systems of Linear Differential Equations with Truncated Power Series in the Role of Coefficients

Abstract

Systems of linear ordinary differential equations with the coefficients in the form of infinite formal power series are considered. The series are represented in a truncated form, with the truncation degree being different for different coefficients. Induced recurrent systems and literal designations for unspecified coefficients of the series are used as a tool for studying such systems. An algorithm for constructing Laurent solutions of the system is proposed for the case where the determinant of the leading matrix of the induced system is not zero and does not contain literals. The series included in the solutions are still truncated. The algorithm finds the maximum possible number of terms of the series that are invariant with respect to any prolongations of the truncated coefficients of the original system. The implementation of the algorithm as a Maple procedure and examples of its usage are presented.