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ABSTRACT

A consistency analysis of differential equation systems involves a sequence of differential - algebraic operations. At present there are know two methods: the Cartan's and the Riquier-Janet-Kuranishi(RJK) method which are equivalent. The implementation of the both of the methods with the purpose of their practical application leads to large symbolic computations which often cannot be performed without a computer. The problem on the consistency investigation of a specific overdetermined system was solved in [1] with the aid of a computer. More recently, a number of computer codes implementing the both of the above methods on a computer have been developed (for example [2]). In the present paper we propose a realization of the RJK algorithm the REDUCE system [3]. One of RJK algorithm advantages over Cartan's algorithm is that there is no need to go over to exterior differential equation. It is, therefore more economical, particularly in the use of computer memory, which, in the problem at hand, is very important. The proposed version of the computer code enables us to investigate only the systems of quasilinear first - order differential equations. This limitation is not very restrictive, because the non-linearity is taken into account only in the process of the computation of the ranks of matrices. The REDUCE program was also used by the present authors for the extraction and construction of exact solutions of the equation systems from the continuum mechanics. New results were obtained with the aid of a computer. V.S. Shurygin and N.N. Yanenko: On the computer implementation of algebraic-differential algorithms. Problemy Kibernetik, Vyp. 6, 1961. V.G. Ganzha, S.V. Meleshko, F.A. Murzin, V.P. Shapeev, N.N Yanenko: Realization on computer of an algorithm for studying the consistency of partial differential equations. Dokl. Acad. Nauk SSSR, vol. 261, No 5, 1981. [3]. A.C. Hearn: REDUCE User's Manual. 1985.

REFERENCES

• 1: V.S. Shurygin and N.N. Yanenko: On the computer implementation of algebraic-differential algorithms. Problemy Kibernetik, Vyp. 6, I961.
• 2: V.G. Ganzha, S.V. Meleshko, F.A. Murzin, V.P. Shapeev, N.N Yanenko: Realization on computer of an algorithm for studying the consistency of partial differential equations. Dokl. Acad. Nauk SSSR, vol. 261, No 5, 1981.
• 3: A.C. Hearn: REDUCE User' s Manual. 1985.

INDEX TERMS

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

          Nouns: REDUCE

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

General Terms:
Algorithms