Analytical solution of Abel integral equation arising in astrophysics via Laplace transform | ||||
Journal of the Egyptian Mathematical Society | ||||
Volume 23, Issue 1, 2015, Page 102-107 PDF (588.44 K) | ||||
Document Type: Original Article | ||||
DOI: 10.1016/j.joems.2014.02.004 | ||||
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Authors | ||||
Sunil Kumar* 1; Amit Kumar1; Devendra Kumar2; Jagdev Singh3; Arvind Singh4 | ||||
1Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India | ||||
2Department of Mathematics, Jagan Nath Gupta Institute of Engineering and Technology, Jaipur 302022, Rajasthan, India | ||||
3Department of Mathematics, Jagan Nath University, Village-Rampura, Tehsil-Chaksu, Jaipur 303901, Rajasthan, India | ||||
4TDHC-Institute of Hydropiwer Engineering Technology, (IHET) Bhagirathipuram, New Tehri, India | ||||
Abstract | ||||
The main aim of the present work is to propose a new and simple algorithm for Abel integral equation, namely homotopy perturbation transform method (HPTM). The homotopy perturbation transform method is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. Abel’s integral equation occurs in the mathematical modeling of several models in physics, astrophysics, solid mechanics and applied sciences. The numerical solutions obtained by proposed method indicate that the approach is easy to implement and computationally very attractive. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. | ||||
Keywords | ||||
Laplace transform method; Abel’s integral equation; Homotopy perturbation method; Mittag-Leffler function | ||||
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