  Among various methods of finding accessory parameters in the
Schwarz-Christoffel integrals, Kufarev's method, based on the Loewner
differential equation, plays an important role. It is used for describing
one-parameter families of functions that conformally map a canonical domain
onto a polygon with a slit the endpoint of which moves along a polygonal line
starting from a boundary point. We present a modification of Kufarev's method
for the case of several slits, the lengths of which have depend of each other
in a certain way. We justify the method and find a system of ODEs describing
the dynamics of accessory parameters. We also present the results of numerical
calculations which confirm the efficiency of our method.
