Symbolic—numerical computations in the stability analyses of difference schemes

ABSTRACT

We propose a number of symbolic-numeric approaches to the computer aided construction of the stability domains of difference schemes approximating the partial differential equations with constant coefficients. We use the Fourier method, the algebraic methods of the Routh-Hurwitz and Schur-Cohn theories for the localization of the polynomial zeros, the methods of the optimization theory as well as the means of computer algebra, digital image processing and computer graphics. The efficiency of the approaches is demonstrated at the practical examples of difference schemes for the fluid dynamics problems.

REFERENCES

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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
      G.1.8 Partial Differential Equations
          Subjects: Finite difference methods

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

General Terms:
Algorithms, Theory