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In this paper we present a new algorithm for solving linear differential equations in the neighbourhood of an irregular singular point. This algorithm is based upon the same principles as Newton algorithm, however it has a lower cost and is more suitable for computing algebra.
We consider the following problem: given a linear differential system with formal Laurent series coefficients, we want to decide whether the system has non-zero Laurent series solutions, and find all such solutions if they exist. Let us also assume we need only a given positive integer number l of initial terms of these series solutions. How many initial terms of the coefficients of the original system...
We consider linear homogeneous difference equations with rational-function coefficients. The search for solutions in the form of the m-interlacing ( , where L is a given operator) of finite sums of hypergeometric sequences, plays an important role in the Hendriks–Singer algorithm for constructing all Liouvillian solutions of L(y) = 0. We show that Hendriks–Singer’s...
Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We prove that one can effectively construct a left multiple with polynomial coefficients of L such that every singularity of is a singularity of L that is not apparent. As a consequence, if all singularities of L are apparent,...
Abstract. In this paper we describe an efficient algorithm, fully implemented in the Maple computer algebra system, that computes the exponential part of a formal fundamental matrix solution of a linear differential system having a singularity of pole type at the origin.
In this paper we describe an efficient algorithm, fully implemented in the Maple computer algebra system, that computes the exponential part of a formal fundamental matrix solution of a linear differential system having a singularity of pole type at the origin.
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