Here is the equation ETABS uses: P=k*Delta.
3-d matrix analysis programs do not explicitly have to solve for the location of the center of rigidity and calculate applied torsions etc. The force distribution is calculated automatically (including all torsional effects etc) by creating and solving stiffness matrices. Stiffnesses of individual elements, including shearwalls, are determined using the element stiffness formulations (such as K=AE/L for a tension rod).