Let $X$ be a Banach space and $\mathcal{T}$ be an integal operator(both linear and nonlinear) on $X$. consider the problem of solving the integral equation $u-\mathcal{T}u = f$, where $f$ is given and $u$ is the unknown to be determined.
Integral equations arise naturally in applications, in many areas of mathematics, science and technology, and have been studied extensively both at the theoretical and practical level. In general, these equations usually can not be solved explicitly, so one has to use approximation methods to solve the equations. Commonly used approximation methods are projection methods like Galerkin, collocation, Petrov-Galerkin and Nystrom methods. We mainly focus on obtaining superconvergence results for approximate solutions.
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Superconvergence of system of Volterra integral equations by spectral approximation method by Chakraborty S., Nelakanti G. Applied Mathematics and Computation 441 - (2023)
- Co-Principal Investigator
Ph. D. Students
Omprakash Rathore
Area of Research: NUMERICAL FUNCTIONAL ANALYSIS
Sanjoy Kumar Mahato
Area of Research: NUMERICAL FUNCTIONAL ANALYSIS
Shivam Kumar Agrawal
Area of Research: NUMERICAL FUNCTIONAL ANALYSIS
Soumya Das
Area of Research: FUNCTIONAL ANALYSIS
