The differential transformation method and Miller's recurrence

2010/07/13 by Hal Finkel, Finkel, Hal
Mathematics · #Differential Equations and Numerical Methods #Numerical methods for differential equations #math.CA

paper · pdf · doi:10.48550/arxiv.1007.2178

5 pages

arxiv created 2010/07/13 · arxiv updated 2010/07/14

Abstract

The differential transformation method (DTM) enables the easy construction of a power-series solution to a nonlinear differential equation. The exponentiation operation has not been specifically addressed in the DTM literature, and constructing it iteratively is suboptimal. The recurrence for exponentiating a power series by J.C.P. Miller provides a concise implementation of exponentiation by a positive integer for DTM. An equally-concise implementation of the exponential function is also provided.

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