Interpolation results for convergence of implicit Euler schemes with accretive operators

In this paper, we study the nonlinear abstract Cauchy problem with an m-accretive operator. If the initial value and the right-hand side lie in some interpolation sets with parameter \(\alpha \) $\alpha$ , then we obtain the rate of convergence \(O(|\pi |^{\alpha /2})\) $O(|\pi {|}^{\alpha /2})$ for solutions of the corresponding implicit Euler schemes and for the Euler solution as the limit, we obtain Hölder continuity of exponent \(\alpha \) $\alpha$ .