A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations - Mathematical PhysicsReportar como inadecuado




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Abstract: In this paper we discuss three symbolic approaches for the generation of afinite difference scheme of a partial differential equation PDE. We prove,that for a linear PDE with constant coefficients these three approaches areequivalent and discuss the applicability of them to nonlinear PDE-s as well asto the case of variable coefficients. Moreover, we systematically use anothersymbolic technique, namely the cylindrical algebraic decomposition, in order toderive the conditions on the von Neumann stability of a difference s cheme fora linear PDE with constant coefficients. For stable schemes we demonst ratealgorithmic and symbolic approach to handle both continuous and discrete dispersion. We present an implementation of tools for generation of schemes,which rely on Gr\-obner basis, in the system SINGULAR and present numerous examples, computed with our implementation. In the stability analysis, we usethe system MATHEMATICA for cylindrical algebraic decomposition.



Autor: Viktor Levandovskyy, Bernd Martin

Fuente: https://arxiv.org/







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