An interval method for systems of ode

Abstract

Considered is an interval algorithm producing bounds for the solution of the initial value problem for systems of ordinary differential equations $\dot x(t) = f(t,c,x(t))$, x(t_o)=x_o, involving inexact data c, x_o, taking values in given intervals $C = [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{c} ,\bar c]$, resp. $X_o = [\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{x} _o ,\bar x_o ]$. An estimate for the width of the computed inclusion of the solution set is given under the assumption that f is Lipschitzian. In addition, if f is quasi-isotone, the computed bounds converge to the interval hull of the solution set and the order of global convergence is O(h).