Open AccessApproximation of Elliptic Functions by Means of Trigonometric Functions with Applications
Author(s) -
Alvaro H. Salas,
Lorenzo Hernández,
David L. Ocampo R
Publication year - 2021
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2021/5546666
Subject(s) - elliptic function , trigonometric functions , jacobi elliptic functions , mathematics , elementary function , sine , trigonometric integral , trigonometry , elliptic rational functions , nonlinear system , quarter period , jacobian matrix and determinant , elliptic integral , elliptic curve point multiplication , differentiation of trigonometric functions , elliptic curve , algebra over a field , mathematical analysis , pure mathematics , geometry , physics , linear interpolation , polynomial , bicubic interpolation , quantum mechanics
In this work, we give approximate expressions for Jacobian and elliptic Weierstrass functions and their inverses by means of the elementary trigonometric functions, sine and cosine. Results are reasonably accurate. We show the way the obtained results may be applied to solve nonlinear ODEs and other problems arising in nonlinear physics. The importance of the results in this work consists on giving easy and accurate way to evaluate the main elliptic functions cn, sn, and dn, as well as the Weierstrass elliptic function and their inverses. A general principle for solving some nonlinear problems through elementary functions is stated. No similar approach has been found in the existing literature.
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