  A model of high temperature superconducting dynamo, a promising type of flux
pumps capable of wireless injection of a large DC current into a
superconducting circuit, has recently been chosen as an applied
superconductivity benchmark problem and solved using ten different numerical
methods (Ainslie et al 2020 Supercond. Sci. Technol. 33 105009). Using
expansions in Chebyshev polynomials for approximation in space and the method
of lines for integration in time we derive a simple and accurate numerical
method which is much faster. The proposed numerical method was applied also to
problems with transport current and a field-dependent sheet critical current
density.
