A stable and accurate convective modelling procedure based on quadratic upstream interpolation
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Digital image processing
Automatic generation of finite difference equations and fourier stability analyses
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
A new symbolic-numeric approach to stability analysis of difference schemes
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
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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.