Validated solutions of initial value problems for parametric ODEs

Complexity of parametric initial value problems for systems of ODEs

We study the approximate solution of initial value problems for parameter dependent finite or infinite systems of scalar ordinary differential equations (ODEs). Both the deterministic and the randomized setting is considered, with input data from various smoothness classes. We study deterministic and Monte Carlo multilevel algorithms and derive convergence rates. Moreover, we prove their optima...

Validated solutions of initial value problems for ordinary differential equations

Compared to standard numerical methods for initial value problems (IVPs) for ordinary diierential equations (ODEs), validated methods for IVPs for ODEs have two important advantages: if they return a solution to a problem, then (1) the problem is guaranteed to have a unique solution, and (2) an enclosure of the true solution is produced. The authors survey Taylor series methods for validated so...

Validated Solution of Initial Value Problems for ODEs with Interval Parameters

In initial value problems for ODEs with interval-valued parameters, it is desirable in many applications to be able to determine a validated enclosure of all possible solutions to the ODE system. Much work has been done for the case in which initial values are given by intervals, and there are several available software packages that deal with this case. However, relatively little work has been...

Initial Value Problems for ODEs in Problem Solving Environments

The problem solving environments (PSEs) Maple [8] and Matlab [7] are in very wide use. Although they have much in common, they are clearly distinguished by the emphasis in Maple on algebraic computation and in Matlab on numerical computation. We discuss here a program, IVPsolve, for solving numerically initial value problems (IVPs) for systems of first order ordinary differential equations (ODE...

Parallel Implementation of a Validated Method for Initial Value Problems