A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution
This paper proposes a fractional model for nonlinear waves in hyperelastic rods, which describes far-field, finite length, finite amplitude radial deformation waves in cylindrical compressible hyperelastic rods. In this model, fractional derivatives are described in the Caputo sense. The error anal...
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doaj-cb0fbc9870aa48d99cbfbd7c54abdb262020-11-25T01:40:10ZengWalailak UniversityWalailak Journal of Science and Technology1686-39332228-835X2014-01-01111110.2004/wjst.v11i12.448429A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate SolutionSunil KUMAR0Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand 801014 This paper proposes a fractional model for nonlinear waves in hyperelastic rods, which describes far-field, finite length, finite amplitude radial deformation waves in cylindrical compressible hyperelastic rods. In this model, fractional derivatives are described in the Caputo sense. The error analysis shows that our approximate solution converges very rapidly to the exact solution and the numerical solution is compared with the known analytical solution which is nearly identical with the exact solution. The method introduces a promising tool for solving time the fractional hyperelastic rod equation. doi:10.14456/WJST.2014.71 http://wjst.wu.ac.th/index.php/wjst/article/view/448Hyperelastic rodfractional derivativeanalytic approximate solutionhomotopy perturbation method |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Sunil KUMAR |
spellingShingle |
Sunil KUMAR A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution Walailak Journal of Science and Technology Hyperelastic rod fractional derivative analytic approximate solution homotopy perturbation method |
author_facet |
Sunil KUMAR |
author_sort |
Sunil KUMAR |
title |
A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution |
title_short |
A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution |
title_full |
A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution |
title_fullStr |
A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution |
title_full_unstemmed |
A New Mathematical Model for Nonlinear Wave in a Hyperelastic Rod and Its Analytic Approximate Solution |
title_sort |
new mathematical model for nonlinear wave in a hyperelastic rod and its analytic approximate solution |
publisher |
Walailak University |
series |
Walailak Journal of Science and Technology |
issn |
1686-3933 2228-835X |
publishDate |
2014-01-01 |
description |
This paper proposes a fractional model for nonlinear waves in hyperelastic rods, which describes far-field, finite length, finite amplitude radial deformation waves in cylindrical compressible hyperelastic rods. In this model, fractional derivatives are described in the Caputo sense. The error analysis shows that our approximate solution converges very rapidly to the exact solution and the numerical solution is compared with the known analytical solution which is nearly identical with the exact solution. The method introduces a promising tool for solving time the fractional hyperelastic rod equation.
doi:10.14456/WJST.2014.71
|
topic |
Hyperelastic rod fractional derivative analytic approximate solution homotopy perturbation method |
url |
http://wjst.wu.ac.th/index.php/wjst/article/view/448 |
work_keys_str_mv |
AT sunilkumar anewmathematicalmodelfornonlinearwaveinahyperelasticrodanditsanalyticapproximatesolution AT sunilkumar newmathematicalmodelfornonlinearwaveinahyperelasticrodanditsanalyticapproximatesolution |
_version_ |
1725046645381398528 |