Approximation of Elliptic Functions by Means of Trigonometric Functions with Applications
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...
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| Veröffentlicht in: | Mathematical problems in engineering 2021-10, Vol.2021, p.1-16 |
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| creator | Salas, Alvaro H. Martinez, Lorenzo J. H. Ocampo R., David L. R. |
| description | 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. |
| doi_str_mv | 10.1155/2021/5546666 |
| format | Article |
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H. ; Ocampo R., David L. R.</creator><contributor>M. A. Khater, Mostafa</contributor><creatorcontrib>Salas, Alvaro H. ; Martinez, Lorenzo J. H. ; Ocampo R., David L. R. ; M. A. Khater, Mostafa</creatorcontrib><description>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.</description><identifier>ISSN: 1024-123X</identifier><identifier>EISSN: 1563-5147</identifier><identifier>DOI: 10.1155/2021/5546666</identifier><language>eng</language><publisher>New York: Hindawi</publisher><subject>Algebra ; Approximation ; Elliptic functions ; Helmholtz equations ; Integrals ; Mathematical problems ; Physics ; Trigonometric functions ; Weierstrass functions</subject><ispartof>Mathematical problems in engineering, 2021-10, Vol.2021, p.1-16</ispartof><rights>Copyright © 2021 Alvaro H. Salas et al.</rights><rights>Copyright © 2021 Alvaro H. Salas et al. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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| source | Wiley Online Library Open Access; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection |
| subjects | Algebra Approximation Elliptic functions Helmholtz equations Integrals Mathematical problems Physics Trigonometric functions Weierstrass functions |
| title | Approximation of Elliptic Functions by Means of Trigonometric Functions with Applications |
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