Area of research during my Ph. D.:
I completed my doctoral research (Jan 2004 to Jan 2009) in the area of applied Mathematics from IIT Roorkee. I mathematically modelled some problems of fracture mechanics. After modeling, the resulted partial differential equations were solved with the help of Fourier transform which got reduced first in to a pair of dual integral equation and finally into a Fredholm integral equation of second kind. This integral equation was numerically solved with the help of quadrature method. The obtained results were analysed and conclusions were drawn.
Area of research during my Post doc at University of Louisiana, USA:
I worked as a post doctoral fellow at University of Louisiana, USA from July 31, 2013 to July 30, 2014. During this period I worked on numerical methods to solve fractional order differential equations by using wavelets.
Details of Ph. D. awarded under my supervision:
1) Mr. Bijil Prakash was awarded Ph. D. degree in the convocation held at BITS Pilani K K Birla Goa Campus, Goa, on August 05, 2018. The title of the his thesis was "Application of Haar Wavelets Based Numerical Methods to Mathematical Models in Fractional Calculus". His Ph. D. viva-voce exam was held on 3rd July 2018 (Examiners: Prof. Mani Mehra, IIT, Delhi and Prof. B. V. Rathish Kumar, IIT Kanpur).
2. 2) Mrs. Vaishali Sharma was awarded Ph. D. degree in the convocation held at BITS Pilani K K Birla Goa Campus, Goa, on August 11, 2019. The title of her thesis was "Numerical methods for solving singular integral equations and its applications. Her Ph. D. viva-voce exam was held on October 09, 2018 (Examiners: Prof. Rekha P. Kulkarni, IIT Bombay and Prof. D. Bahuguna, IIT Kanpur).
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