Purpose – To provide a reliable numerical technique for the time integration of the electromagnetic models with sinusoidal excitation.
Design/methodology/approach – The numerical integration of an electrotechnical problem is commonly carried out using adaptive time stepping. For one particular selected time step, Runge-Kutta (RK) adaptive integration methods deliver two approximations to the solution with different order of approximation. The difference between both is used to estimate the local error.
Findings – Standard error-controlled RK time integration fails for electromagnetic problems with sinusoidal excitation when the adaptive time step selection relies upon the comparison of a main solution and an embedded solution where the difference of orders is one. This problem is overcome when the embedded solution differs by two orders of approximations. Such embedded solution is efficiently constructed by putting appropriate order conditions on the coefficients of the Butcher table.
Originality/value – Using the technique proposed in the paper, electromagnetic problems with sinusoidal dynamics can also be effectively tackled.