Computation of the Strength of PDEs of Mathematical Physics and their Difference Approximations

摘要: We develop a method for evaluation of A. Einstein's strength systems partial differential and difference equations based on the computation Hilbert-type dimension polynomials associated field extensions. Also we present algorithms such computations, which are Grobner basis adjusted modules over rings differential, inversive operators. The developed technique is applied to some fundamental PDEs mathematical physics as diffusion equation, Maxwell an electromagnetic given by its potential. In each these cases determine original system corresponding obtained forward symmetric schemes. particular, obtain comparing two schemes from point view their strength.