Ordinary Differential Equations

Abstract

Session Ordinary-Differential-Equations formalizes ordinary differential equations (ODEs) and initial value problems. This work comprises proofs for local and global existence of unique solutions (Picard-Lindelöf theorem). Moreover, it contains a formalization of the (continuous or even differentiable) dependency of the flow on initial conditions as the flow of ODEs. Not in the generated document are the following sessions: • HOL-ODE-Numerics: Rigorous numerical algorithms for computing enclosures of solutions based on Runge-Kutta methods and affine arithmetic. Reachability analysis with splitting and reduction at hyperplanes. • HOL-ODE-Examples: Applications of the numerical algorithms to concrete systems of ODEs (e.g., van der Pol and Lorenz attractor).