This paper investigates methods for composing difference approximations to form one-step and many-step parallel difference schemes of a given order, with a focus on numerically solving the Cauchy problem for both ordinary differential equations and evolutionary partial differential equations. The proposed discrete approximations allow for varying the order of error while moving away from the maximum possible on a fixed set of knots, while ensuring the absolute or A- \(\alpha \) stability of the numerical solutions. It is shown that one-step schemes of the maximum approximation order remain absolutely stable as the dimensionality of computational blocks increases. Fulfilment of the condition of absolute or A- \(\alpha \) stability for multistep methods is provided by reducing the maximum possible order of approximation.