@article{KO1983157,
    Abstract = {The computational complexity of the solution y of the differential equation y′(x) = f(x, y(x)), with the initial value y(0) = 0, relative to the computational complexity of the function f is investigated. The Lipschitz condition on the function f is shown to play an important role in this problem. On the one hand, examples are given in which f is polynomial time computable but none of the solutions y is computable. On the other hand, if f is polynomial time computable and if f satisfies a weak form of the Lipschitz condition then the (unique) solution y is polynomial space computable. Furthermore, there exists a polynomial time computable function f which satisfies this weak Lipschitz condition such that the (unique) solution y is not polynomial time computable unless P = PSPACE.},
    Author = {Ko, Ker-I},
    File = {On the computational complexity of ordinary differential equations - 1-s2.0-S001999588380062X-main - p.pdf},
    ISSN = {0019-9958},
    Journal = {Information and Control},
    Number = {1},
    Pages = {157-194},
    Title = {On the computational complexity of ordinary differential equations},
    URL = {https://www.sciencedirect.com/science/article/pii/S001999588380062X},
    Volume = {58},
    Year = {1983},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S001999588380062X},
    bdsk-url-2 = {https://doi.org/10.1016/S0019-9958(83)80062-X},
    date-added = {2021-02-17 17:32:19 +0100},
    date-modified = {2021-02-17 17:32:19 +0100},
    doi = {10.1016/S0019-9958(83)80062-X}
}

@article{KO1983157, Abstract = {The computational complexity of the solution y of the differential equation y′(x) = f(x, y(x)), with the initial value y(0) = 0, relative to the computational complexity of the function f is investigated. The Lipschitz condition on the function f is shown to play an important role in this problem. On the one hand, examples are given in which f is polynomial time computable but none of the solutions y is computable. On the other hand, if f is polynomial time computable and if f satisfies a weak form of the Lipschitz condition then the (unique) solution y is polynomial space computable. Furthermore, there exists a polynomial time computable function f which satisfies this weak Lipschitz condition such that the (unique) solution y is not polynomial time computable unless P = PSPACE.}, Author = {Ko, Ker-I}, File = {On the computational complexity of ordinary differential equations - 1-s2.0-S001999588380062X-main - p.pdf}, ISSN = {0019-9958}, Journal = {Information and Control}, Number = {1}, Pages = {157-194}, Title = {On the computational complexity of ordinary differential equations}, URL = {https://www.sciencedirect.com/science/article/pii/S001999588380062X}, Volume = {58}, Year = {1983}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S001999588380062X}, bdsk-url-2 = {https://doi.org/10.1016/S0019-9958(83)80062-X}, date-added = {2021-02-17 17:32:19 +0100}, date-modified = {2021-02-17 17:32:19 +0100}, doi = {10.1016/S0019-9958(83)80062-X} }