Abstract:
Traditional difference schemes are based on the interpolation of grid functions by a polynomial of finite degree. The error of such schemes decreases as a certain degree of step. In this paper, we propose a fundamentally new class of difference schemes with exponential convergence, which is dramatically faster than the traditional power-law one. The typical accuracy gain is 5–8 orders of magnitude or more. The proposed approach is uniformly applicable to various classes of mathematical physics problems and is demonstrated by the example of boundary value problems for ODEs. Examples illustrating the advantages of the proposed approach are given.
