  This paper deals with the solution of delay differential equations describing
evolution of dislocation density in metallic materials. Hardening, restoration,
and recrystallization characterizing the evolution of dislocation populations
provide the essential equation of the model. The last term transforms ordinary
differential equation (ODE) into delay differential equation (DDE) with strong
(in general, H\"older) nonlinearity. We prove upper error bounds for the
explicit Euler method, under the assumption that the right-hand side function
is H\"older continuous and monotone which allows us to compare accuracy of
other numerical methods in our model (e.g. Runge-Kutta), in particular when
explicit formulas for solutions are not known. Finally, we test the above
results in simulations of real industrial process.
