A reliable hybrid numerical method for a time dependent vibration model of arbitrary order

Amit Prakash; Manish Goyal; Haci Mehmet Baskonus; Shivangi Gupta; Amit Prakash; Manish Goyal; Haci Mehmet Baskonus; Shivangi Gupta

doi:10.3934/math.2020068

AIMS Mathematics

2020, Volume 5, Issue 2: 979-1000. doi: 10.3934/math.2020068

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A reliable hybrid numerical method for a time dependent vibration model of arbitrary order

1.
Department of Mathematics, National Institute of Technology, Kurukshetra-136119, India
2.
Department of Mathematics, Institute of Applied Sciences and Humanities, GLA University, Mathura-281406, India
3.
Department of Mathematics and Science Education, Harran University, Sanliurfa, Turkey

Received: 15 October 2019 Accepted: 19 December 2019 Published: 08 January 2020
MSC : 35Q99, 44A99

In this article, the solution of vibration equation of fractional order is found numerically for the large membranes using a powerful technique namely q-homotopy analysis Sumudu transform technique. The parameter ħ suggests a convenient way to control convergence region. The given numerical examples depict competency and accuracy of this scheme. The results are discussed using figures taking diverse wave velocities and initial conditions. Results are also compared with other methods. The outcome divulges that q-HASTM is highly reliable, more efficient, attractive, easier to use as well as highly effective.
Citation: Amit Prakash, Manish Goyal, Haci Mehmet Baskonus, Shivangi Gupta. A reliable hybrid numerical method for a time dependent vibration model of arbitrary order[J]. AIMS Mathematics, 2020, 5(2): 979-1000. doi: 10.3934/math.2020068

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Abstract

In this article, the solution of vibration equation of fractional order is found numerically for the large membranes using a powerful technique namely q-homotopy analysis Sumudu transform technique. The parameter ħ suggests a convenient way to control convergence region. The given numerical examples depict competency and accuracy of this scheme. The results are discussed using figures taking diverse wave velocities and initial conditions. Results are also compared with other methods. The outcome divulges that q-HASTM is highly reliable, more efficient, attractive, easier to use as well as highly effective.

References

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