Biography
Dr. Pratibhamoy Das
Dr. Pratibhamoy Das
Department of Mathematics, Indian Institute of Technology, India
Title: Residual Minimization based Solution Approximations of Weakly Singular Volterra Integro Differential Equations
Abstract: 
In this talk, I focus on the optimal solution approximations of the weakly singular Volterra integro differential equations. First, the sufficient conditions for the existence and uniqueness of the solution of this problem will be considered under different norms. In addition, another, sufficient condition under which the model problem will provide an analytic solution, will be also provided. Next, an operator based parameterized method will be introduced to generate an approximate solution of this problem. This approximate solution is optimized based on least square method. For this, residual minimization is used to obtain the optimal values of the auxiliary parameter.  Experimental results based on the standard methods and residual minimization based optimized methods show the better accuracy of the present method.
Biography: 
Dr. Pratibhamoy Das is an Assistant Professor of Department of Mathematics, Indian Institute of Technology Patna. He works mainly on the optimal accurate numerical analysis of singularly perturbed differential equations and approximations of fractional integro differential equations. Presently, he is working on the a posteriori estimate generation for system of boundary/interior layer originated parabolic problems and theoretical aspects and least square based optimal accurate solutions for fractional integro differential models.
Before joining to IIT Patna, he was an Einstein Foundation Fellow at Institute fur Mathematik, Technische Universitat Berlin, Germany, where he worked with the group of Prof. Volker Mehrmann. He was also a visiting faculty at IISER Bhopal and NBHM Fellow at Indian Institute of Science Bangalore. He did his master from IIT Bombay and doctorate from IIT Guwahati.  At present, he has plenty of international MathScinet and SCI listed publications and single author publications. He is also receipt of several awards, including Young Scientist Award at 100th Indian Science Congress and also DAAD Research Ambassador of Germany.