1. Modeling of geochemical processes Linear system of differential equations
J. Faimon

2. Modeling of geochemical processes Dynamic models
Matrix K is diagonalized into
. Then
Multiplying by U-1 from left side gives
Because U-1 is a matrix of constants, it is
Let us substitute for Then
This equation can be split into a set of individual equations, ,
which can be solved at initial conditions, t = 0, y = y0 as

3. Modeling of geochemical processes Dynamic models
The set of the equations can be expressed in vectors as
and, after re-substitution, as
Multiplying matrix U from left side gives the expression for vector x

4. Modeling of geochemical processes Dynamic models
Example: system of differential equations
Initial conditions: t = 0, x1 = 1 x2 = -1

5. Modeling of geochemical processes Dynamic models
In general: