An Interval Method for System of ODE

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(to)=xo, involving inexact data c, xo, 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).