Stability propagation matrix

Equations (10.36) and (10.37) form a set of autonomous systems. For certain values of the rate propagation matrix, using eigenvectors and stability analysis it can be shown that periodic solutions may result. The initial conditions of the monomers can be represented by... 

Prom this formula we see how the global error of a multistep method is built up. There is in every step a (local) contribution M , which is of the size of the local residual. Therefore, a main task is to control the integration in such a way that this contribution is kept small. The effect of these local residuals on the global error is influenced by n h)- The local effects can be damped or amplified depending on the properties of the propagation matrix n( )- This leads to the discussion of the stability properties of the method and its relation to the stability of the problem. 

One way to avoid the stabilization problem just mentioned is to propagate the log derivative matrix Y(R) [43]. This is defined by... 

Ceramic composites, which use ceramic fiber or whisker reinforcement in a ceramic matrix, are less susceptible to brittle failure since the reinforcement intercepts, deflects and slows crack propagation. At the same time, the load is transferred from the matrix to the fibers to be distributed more uniformly. These ceramic composites are characterized by low density, generally good thermal stability, and corrosion resistance. 

---