Gevrey and analytic convergence of Picard's successive approximations

초록

Picard's successive approximation of an ordinary differential equation converges in the Gevrey sense to the solution of ODE if the given vector field is a Gevrey mapping. Also it converges analytically if the vector field is analytic. This extends a result of A. J. Izzo (1999) who showed the C-r-convergence of Picard's successive approximation.

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