  We develop an efficient method for solving transport equations, particularly
in the context of electroweak baryogenesis. It provides fully-analytical
results under mild approximations and can also test semi-analytical results,
which are applicable in more general cases. Key elements of our method include
the reduction of the second-order differential equations to first order,
representing the set of coupled equations as a block matrix of the particle
densities and their derivatives, identification of zero modes, and block
decomposition of the matrix. We apply our method to calculate the baryon
asymmetry of the Universe (BAU) in a Standard Model effective field theory
framework of complex Yukawa couplings to determine the sensitivity of the
resulting BAU to modifications of various model parameters and rates, and to
estimate the effect of the commonly-used thin-wall approximation.
