TY - GEN
T1 - On the complexity of solving initial value problems
AU - Bournez, Olivier
AU - Graça, Daniel S.
AU - Pouly, Amaury
PY - 2012/12/1
Y1 - 2012/12/1
N2 - In this paper we prove that computing the solution of an initial-value problem ẏ = p(y) with initial condition y(t0) = y0 ε R d 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 = supt0≤u≤T y(u)∞. 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.
AB - In this paper we prove that computing the solution of an initial-value problem ẏ = p(y) with initial condition y(t0) = y0 ε R d 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 = supt0≤u≤T y(u)∞. 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.
UR - https://www.scopus.com/pages/publications/84874996606
U2 - 10.1145/2442829.2442849
DO - 10.1145/2442829.2442849
M3 - Conference contribution
AN - SCOPUS:84874996606
SN - 9781450312691
T3 - Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
SP - 115
EP - 121
BT - ISSAC 2012 - Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
T2 - 37th International Symposium on Symbolic and Algebraic Computation, ISSAC 2012
Y2 - 22 July 2012 through 25 July 2012
ER -