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

Kumar, Sunil; Kumar, Amit; Kumar, Devendra; Singh, Jagdev; Singh, Arvind

doi:10.1016/j.joems.2014.02.004

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

Document Type : Original Article

Authors

¹ Department of Mathematics, National Institute of Technology, Jamshedpur 831014, Jharkhand, India

² Department of Mathematics, Jagan Nath Gupta Institute of Engineering and Technology, Jaipur 302022, Rajasthan, India

³ Department of Mathematics, Jagan Nath University, Village-Rampura, Tehsil-Chaksu, Jaipur 303901, Rajasthan, India

⁴ TDHC-Institute of Hydropiwer Engineering Technology, (IHET) Bhagirathipuram, New Tehri, India

10.1016/j.joems.2014.02.004

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