Order conditions for linearly implicit fractional step Runge-Kutta methods

In this paper, we study the consistency of a variant of fractional step Runge-Kutta methods. These methods are designed to integrate efficiently semi-linear multidimensional parabolic problems by means of linearly implicit time integration processes. Such time discretization procedures are also related to a splitting of the space differential operator (or the spatial discretization of it) as a sum of 'simpler' linear differential operators and a nonlinear term.