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- Paul G. Warne, Debra Polignone Warne, James S. Sochacki, G. Edgar Parker, D. C. Carothers
- Computers & Mathematics with Applications
- 2006

- David Carothers, William Ingham, +24 authors David Wilk
- 2007

This paper discusses how to pose an initial value problem (IVP) ordinary differential equation (ODE) y = F (t, y); y(t 0) = y 0 , where F : R n → R n in such a way that a modification of Picard's method will generate the Taylor series solution. We extend the result to the IVP partial differential equation (PDE) We discuss how to use the method to determine… (More)

In [7] and [8], Parker and Sochacki considered iterative methods for computing the power series solution to y = G • y where G is a polynomial from R n to R n , including truncations of Picard iteration. The authors demonstrated that many ODE's may be transformed into computationally feasible polynomial problems of this type, and the methods generalize to a… (More)

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