Local approximation study of difference operators by means of REDUCE system

ABSTRACT

This work is devoted to the description of new algorithms and programs in the REDUCE system for the automated study of a local order of the approximation of difference operator written on non-orthogonal meshes. The performance of the program is demonstrated by local approximation of several difference operators in one and two-dimensional cases.

REFERENCES

• 1: Cloutman L.D. and Fullerton L.%4.- Automated Heuristic Stability Analysis for Non-Linear Equation. Los Alamos Scientific Laboratory, Los Almos 1977.
• 2: Michael C. Wirth, Automatic generation of finite difference equations and fourier stability analyses, Proceedings of the fourth ACM symposium on Symbolic and algebraic computation, p.73-78, August 05-07, 1981, Snowbird, Utah, United States [doi>10.1145/800206.806373]
• 3: Valiullin A.N., Ganzha V.G., Meleshko S.V., Murzin F.A., Shapeev V.P., Yanenko N.N.: Symbolic Nanipulations in the Nethod$ of Mathematical Physics. Proceeding Mathematics for Computer Science, Paris, pp. 431-438, 1982.
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INDEX TERMS

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

          Nouns: REDUCE

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on polynomials

  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms
          Subjects: Algebraic algorithms

General Terms:
Algorithms, Languages, Performance