On convergence of difference schemes for delay parabolic equations

The convergence of difference schemes for the approximate solutions of the initial-boundary value problem for the delay parabolic differential equation {dv(t)dt+Av(t)=B(t)v([email protected]),t>=0,v(t)=g(t)([email protected]@[email protected]?0) in an arbitrary Banach space E with the unbounded linear operators A and B(t) in E with dense domains D(A)@?D(B(t)) is investigated. Theorems on convergence estimates for the solutions of the first and the second order of accuracy difference schemes in fractional spaces E"@a are established. In practice, the convergence estimates in Holder norms for the solutions of difference schemes of the first and the second order of approximation in t of the approximate solutions of multi-dimensional delay parabolic equations are obtained. The theoretical statements for the solution of these difference schemes are supported by the numerical example.

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