Addition theorems for ODE. application to evaluation of the Weierstrass function

Abstract

In this paper we present an alternative approach to computing elliptic functions in the real domain. We show that the addition theorem associated with Weierstrass elliptic functions allows us to compute them efficiently. We analyze the basic properties of Weierstrass elliptic functions and their relation to Jacobi elliptic functions. We implement the methodology of argument reduction and reconstruction for the evaluation of Weierstrass functions through the duplication algorithm. Finally, this research aims to improve our understanding of the efficiency of the duplication algorithm for future practical scenarios.