On the complexity of solving initial value problems
Olivier Bournez, Daniel Silva Graça, Amaury Pouly · 2012
In this paper we prove that computing the solution of an initial-value problem y = p(y) with initial condition y(t0) = y0 ∈ Rd at time t0 + T with precision 2−μ where p is a vector of polynomials can be done in time polynomial in the value of T, μ and Y = [equation]. Contrary to existing results, our algorithm works over any bounded or unbounded domain. Furthermore, we do not assume any Lipschitz condition on the initial-value problem.