initial t_step and trunction error

[jieta...@gmail.com]

Dear expokit users/developers,

I'm using the expokit in matlab, and I have several questions about mexpv.m.

(1) It is about the initial step length,and I want to know why it is calulated by this formula (blue codes)and is there any referance for that?

        fact = (((m+1)/exp(1))^(m+1))*sqrt(2*pi*(m+1));

        t_new = (1/anorm)*((fact*tol)/(4*beta*anorm))^xm;

        s = 10^(floor(log10(t_new))-1); t_new = ceil(t_new/s)*s; 

        sgn = sign(t); istep = 0;

         t_step = min( t_out-t_now,t_new );

(2)It is about the local truncation error. I want to know why it is called "small step size :quick convergence" when err1>>err2 ,as well as the situation for err1>err2.

        Thanks.

best regads,

Jessie