\input zb-basic
\input zb-ioport
\iteman{io-port 05270754}
\itemau{Mahmoud, Sayed; Chen, Xiaojun}
\itemti{A verified inexact implicit Runge-Kutta method for nonsmooth ODEs.}
\itemso{Numer. Algorithms 47, No. 3, 275-290 (2008).}
\itemab
Consider the system ${{dp(t,u)}\over{dt}}=f(t,u)$, $t\geq 0$, $u(0)=u_0$, where $p:(0,\infty)\times D\rightarrow\Bbb R^n$ is a continuously differentiable function, $f:(0,\infty)\times D\rightarrow\Bbb R^n$ is Lipschitz continuous but not necessarily differentiable, $u\in\Bbb R^n$ and $D$ is a compact set in $\Bbb R^n$. Generally, an exact solution of these nonsmooth equations cannot be obtained when using implicit Runge-Kutta (IRK) methods.  A verified inexact IRK method for nonsmooth ordinary differential equations (ODEs) is proposed. It computes a global error bound for the inexact solution. The dependence of the error of such solution on the radius containing the exact solution is proved. Nontrivial numerical experiments show the efficiency of the proposed algorithm. The problem appears in earthquake-induced structural pounding and oscillations.
\itemrv{Lubom\'\i r Bakule (Praha)}
\itemcc{}
\itemut{verification of solution; nonsmooth ODEs; structural pounding; oscillations}
\itemli{doi:10.1007/s11075-008-9180-0}
\end