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Among various methods of finding accessory parameters in theSchwarz-Christoffel integrals, Kufarev's method, based on the Loewnerdifferential equation, plays an important role. It is used for describingone-parameter families of functions that conformally map a canonical domainonto a polygon with a slit the endpoint of which moves along a polygonal linestarting from a boundary point. We present a modification of Kufarev's methodfor the case of several slits, the lengths of which have depend of each otherin a certain way. We justify the method and find a system of ODEs describingthe dynamics of accessory parameters. We also present the results of numericalcalculations which confirm the efficiency of our method.

One-parameter families of conformal mappings of the half-plane onto polygonal domains with several slits