I am reading the journal article” A New Unconditionally Stable FDTD Method Based on the Newmark-Beta Algorithm”, and trying to derive its relative formulation. I came across the following iteration equation: (as in the attachment Question 1 Pic 1.jpg)
The Left Hand Side (LHS) includes unknown fields Eρ (ρ=x,y,z) while the Right Hand Side is known. There are three sets of such equations. The paper says that such equations could be transformed into the following form: (as in attachment Question 1 Pic 2.jpg)
But how? Literature recommendations on the topic are also appreciated.