Regular solutions of linear differential systems with power series coefficients

Authors:
S. A. Abramov;D. E. Khmelnov
Affiliations:
Computing Center, Russian Academy of Sciences, Moscow, Russia 119333;Computing Center, Russian Academy of Sciences, Moscow, Russia 119333
Venue:
Programming and Computing Software
Year:
2014

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Abstract

The following problem is considered: given a system of linear ordinary differential equations of arbitrary order with power series coefficients, to recognize whether it has regular solutions at point 0 and, if it does, to find them. An algorithm for solving this problem is proposed. Each power series that is a coefficient of the original system is specified by a procedure that computes the series coefficient by the index of this coefficient. The original system is assumed to have full rank; i.e., the equations of the system are independent. The algorithm is implemented in Maple.