Addition theorems for Ck real functions and applications in ordinary differential equations
Abstract
This work establishes the existence of addition theorems and double-angle formulas for Ck real scalar functions. Moreover, we determine necessary and sufficient conditions for a bivariate function to be an addition formula for a Ck real function. The double-angle formulas allow us to generate a duplication algorithm, which can be used as an alternative to the classical numerical methods to obtain an approximation for the solution of an ordinary differential equation. We demonstrate that this algorithm converges uniformly in any compact domain contained in the maximal domain of that solution. Finally, we carry out some numerical simulations showing a good performance of the duplication algorithm when compared with standard numerical methods
Keywords
Cite
@article{arxiv.2012.04168,
title = {Addition theorems for Ck real functions and applications in ordinary differential equations},
author = {Francisco Crespo and Salomón Rebollo-perdomo and Jorge L. Zapata},
journal= {arXiv preprint arXiv:2012.04168},
year = {2020}
}
Comments
20 pages, 7 figures