• Corpus ID: 37156287

# Application of the Bernstein Polynomials for Solving Volterra Integral Equations with Convolution Kernels

```@inproceedings{Alt2016ApplicationOT,
title={Application of the Bernstein Polynomials for Solving Volterra Integral Equations with Convolution Kernels},
author={A. Alt},
year={2016}
}```
• A. Alt
• Published 2016
• Mathematics
In this article, we consider the second-type linear Volterra integral equations whose kernels based upon the di erence of the arguments. The aim is to convert the integral equation to an algebraic one. This is achieved by approximating functions appearing in the integral equation with the Bernstein polynomials. Since the kernel is of convolution type, the integral is represented as a convolution product. Taylor expansion of kernel along with the properties of convolution are used to represent…
5 Citations
• Mathematics, Computer Science
2020 15th International Conference on Computer Engineering and Systems (ICCES)
• 2020
A modified formula of the traditional Barycentric Lagrange interpolation is established and applied for solving the second kind Volterra integral equations and it is observed that the interpolant solutions equal to the exact solutions if the kernel and the given functions are analytic while extraordinarily converge to the exactly solutions for non-algebraic functions, which ensures the accuracy and authenticity of the presented method.
• Mathematics
• 2019
The Fredholm integral equations of the first kind are often considered as ill-posed problems. The conventional way of solving them is to first convert them into the Fredholm integral equations of the
• Mathematics
• 2018
In this work, we want to use the Non-polynomial spline basis and Quasi-linearization method to solve the nonlinear Volterra integral equation. When the iterations of the Quasilinear technique
• Computer Science
Physical review. E
• 2023
This work found that Bézier interpolation reduces the estimation bias for both dynamical inference problems: Determining fitness parameters for evolving populations and inferring forces driving Ornstein-Uhlenbeck processes.
• Mathematics
International Journal of Applied and Computational Mathematics
• 2020
In this paper, we investigate the existence and uniqueness of solution for a multi-term fractional integro-differential problem with nonlocal four-point fractional boundary conditions via the Caputo