Consistency of finite difference approximations for linear PDE systems and its algorithmic verification

摘要: In this paper we consider finite difference approximations for numerical solving of systems partial differential equations the form f1 = · fp 0, where F := {f1, ..., fp} is a set linear polynomials over field rational functions with coefficients. For orthogonal and uniform solution grids strengthen generally accepted concept equation-wise consistency (e-consistency) 0 as approximation ones. Instead, introduce notion all consequences polynomial f {f, subset ideal 〈F〉. The last consistency, which call s-consistency (strong consistency), admits algorithmic verification via Grobner basis 〈f〉. Some related illustrative examples approximations, including those are e-consistent s-inconsistent, given.