Operator calculus approach to solving analytic systems

Details Operator calculus approach to solving analytic systems Operator calculus approach to solving analytic systems

2006-07-26

arxiv.org/abs/math/0607649v1

Mathematics in Computer Science Volume 1, Number 2, 239-251, 2007

Mathematics

Classical Analysis and ODEs

3 figures (Maple worksheets)

Scientific paper

10.1007/s11786-007-0011-9

Solving analytic systems using inversion can be implemented in a variety of ways. One method is to use Lagrange inversion and variations. Here we present a different approach, based on dual vector fields. For a function analytic in a neighborhood of the origin in the complex plane, we associate a vector field and its dual, an operator version of Fourier transform. The construction extends naturally to functions of several variables. We illustrate with various examples and present an efficient algorithms readily implemented symbolically in Maple while suitable as well for numerical computations using languages such as C or Java.

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