Seminar Details

Seminar Title
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Numerical solutions for integro-differential equations involving small parameters and fractional derivatives
Seminar Type
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Registration Seminar
Department
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Mathematics
Speaker Type
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Student
Speaker Name
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ABHILIPSA PANDA ( RollNo : 519MA2004)
Date  &  Time
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11 May 2021  11.00AM
Venue
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Online through MS team, Code: j1fiigr
Contact
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Prof. Jugal Mohapatra
Abstract
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In this report, two integro-differential equations are considered. The first model deals with a singularly perturbed Volterra integro-differential equation. A fitted mesh finite difference method is employed using a finite difference scheme for the derivative operator and a composite trapezoidal rule for the integral part on a piecewise-uniform Shishkin mesh. It is proved that the proposed method converges uniformly with respect to the perturbation parameter. Richardson extrapolation is used for improving the accuracy of the computed solution measured in the discrete maximum norm and almost second order convergence is acquired. The second model deals with a fractional partial integro differential equation. Adomian decomposition and homotopy perturbation methods are used to solve the model. The existence and convergence analysis of the solution is also provided. Numerical examples are carried out which are in agreement with the theoretical estimates.