@article{LABELLE1986344,
    Abstract = {We analyse the solution set of first-order initial value differential problems of the form dydx = ƒ(x, y), y(0) = 0 in the context of combinatorial species in the sense of A. Joyal (Adv. in Math.42 (1981), 1--82). It turns out that the situation is much richer than in the case of formal power series: many non-isomorphic combinatorial solutions are possible for a given problem, although they all have the same underlying generating series. We give many examples of this phenomenon and also elaborate a combinatorial Newton-Raphson iterative scheme for the construction of the solutions. The multidimensional case is treated explicitly.},
    Author = {Labelle, Gilbert},
    File = {On combinatorial differential equations - 1-s2.0-0022247X86903100-main - a.pdf},
    ISSN = {0022-247X},
    Journal = {Journal of Mathematical Analysis and Applications},
    Number = {2},
    Pages = {344-381},
    Title = {On combinatorial differential equations},
    URL = {https://www.sciencedirect.com/science/article/pii/0022247X86903100},
    Volume = {113},
    Year = {1986},
    bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0022247X86903100},
    bdsk-url-2 = {https://doi.org/10.1016/0022-247X(86)90310-0},
    date-added = {2023-02-20 12:04:39 +0100},
    date-modified = {2023-02-20 12:04:39 +0100},
    doi = {10.1016/0022-247X(86)90310-0}
}

@article{LABELLE1986344, Abstract = {We analyse the solution set of first-order initial value differential problems of the form dydx = ƒ(x, y), y(0) = 0 in the context of combinatorial species in the sense of A. Joyal (Adv. in Math.42 (1981), 1--82). It turns out that the situation is much richer than in the case of formal power series: many non-isomorphic combinatorial solutions are possible for a given problem, although they all have the same underlying generating series. We give many examples of this phenomenon and also elaborate a combinatorial Newton-Raphson iterative scheme for the construction of the solutions. The multidimensional case is treated explicitly.}, Author = {Labelle, Gilbert}, File = {On combinatorial differential equations - 1-s2.0-0022247X86903100-main - a.pdf}, ISSN = {0022-247X}, Journal = {Journal of Mathematical Analysis and Applications}, Number = {2}, Pages = {344-381}, Title = {On combinatorial differential equations}, URL = {https://www.sciencedirect.com/science/article/pii/0022247X86903100}, Volume = {113}, Year = {1986}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0022247X86903100}, bdsk-url-2 = {https://doi.org/10.1016/0022-247X(86)90310-0}, date-added = {2023-02-20 12:04:39 +0100}, date-modified = {2023-02-20 12:04:39 +0100}, doi = {10.1016/0022-247X(86)90310-0} }