Conservative difference schemes for parabolic equations with time-adaptive grids

Abstract

This paper is devoted to research aspects of the convergence rate of conservative difference schemes (d.s.) with time-adaptive grids in cases, where a space grid is irregular and the third boundary-value problem is considered for one-dimensional linear parabolic equations. The unconditional convergence of created d.s. is proved in a C-metric at the rate O(h²+τ₀ ^1/2).