Solution for Boundedness, Time Period and Graphs of Rate Measures in Matlab of Undamped and Unforced Duffing Equation

Authors

  • Ajaya Kumar Singh  Department of Mathematics, Ekamra College, Bhubaneswar, Odisha, India

DOI:

https://doi.org//10.32628/IJSRST20714

Keywords:

Duffing Equation, Undamped And Unforced, Oscillators, Jacobi Elliptic Functions, Time Period, Boundedness

Abstract

The duffing equation is is a non -linear second order differential equation. In this paper my aim is to solve for boundedness and time period of the duffing equation (undamped ( and unforced / undriven ( )) by Jacobi elliptic functions cn and nc, nd, cd and dc and sn. Also I expressed the identities, the properties and graphs using MATLAB program of three Jacobi elliptic functions. I observed the three special cases solve for boundedness and time period. They are Case A : solve Cubic , Case B : Solve Initial Value Problem for Cubic duffing equation with Special Cases for boundedness and time period which cannot be solved by cosine function. So, it can be solved in the form of in terms of Jacobi elliptic functions cn and nc, dc and cd, nd having positive frequency and modulus in the interval [0, 1]. Case C : Solve Initial Value Problem for Linear . Also for practical and research purposes I introduced the graphs of velocity and acceleration of duffing equation (undamped ( and unforced / undriven ( )) using MATLAB.

References

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International Journal of Scientific Research in Science and Technology

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Published

2020-01-30

Issue

Volume 7, Issue 1, January-February-2020

Section

Research Articles

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Ajaya Kumar Singh, " Solution for Boundedness, Time Period and Graphs of Rate Measures in Matlab of Undamped and Unforced Duffing Equation, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 7, Issue 1, pp.16-27, January-February-2020. Available at doi : https://doi.org/10.32628/IJSRST20714