A parametric transformation at numerical integration of ODE

The initial value problem for ordinary differential equation (ODE) is investigated when the linear parametric transformation (rotation of coordinate axes) is applied. It is shown that for transformed equation the principal term of asymptotic error expansion of numerical method can be minimized by an angle of rotation. The dependence of the optimal angle φ_opt(λ)on λis plotted for the model equation solved by linear multistep methods and Runge-Kutta methods.