An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point

ABSTRACT

We discuss in this paper an algorithm for the computation of the formal solutions of differential systems in the neighborhood of an irregular singular point. In the reduction of the differential systems, we use its Arnold-Wasow's canonical form. We discuss also an algorithm for the reduction of the differential system to its Arnold-Wasow's canonical form. Then we discuss the results of a shearing transformation on this canonical form and we get the convergence of the algorithm. This paper and [3] consist of a complete study of the problem of computations of the formal solutions of differential systems in the neighborhood of a singular point (regular or irregular).

REFERENCES

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• 3: G. Chen , I. Gil, The implementation of an algorithm in Macsyma: computing the formal solutions of differential systems in the neighborhood of regular singular point, Proceedings of the international symposium on Symbolic and algebraic computation, p.307, August 20-24, 1990, Tokyo, Japan [doi>10.1145/96877.96978]
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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.3 Languages and Systems

          Nouns: MACSYMA

General Terms:
Algorithms, Languages