Kumar, S., Kumar, A., Kumar, D., Singh, J., Singh, A. (2015). Analytical solution of Abel integral equation arising in astrophysics via Laplace transform. test, 23(1), 102-107. doi: 10.1016/j.joems.2014.02.004
Sunil Kumar; Amit Kumar; Devendra Kumar; Jagdev Singh; Arvind Singh. "Analytical solution of Abel integral equation arising in astrophysics via Laplace transform". test, 23, 1, 2015, 102-107. doi: 10.1016/j.joems.2014.02.004
Kumar, S., Kumar, A., Kumar, D., Singh, J., Singh, A. (2015). 'Analytical solution of Abel integral equation arising in astrophysics via Laplace transform', test, 23(1), pp. 102-107. doi: 10.1016/j.joems.2014.02.004
Kumar, S., Kumar, A., Kumar, D., Singh, J., Singh, A. Analytical solution of Abel integral equation arising in astrophysics via Laplace transform. test, 2015; 23(1): 102-107. doi: 10.1016/j.joems.2014.02.004

Analytical solution of Abel integral equation arising in astrophysics via Laplace transform

Journal of the Egyptian Mathematical Society
Volume 23, Issue 1, 2015, Pages 102-107    PDF (588.44 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.02.004
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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