• 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… 
pmf.ni.ac.rs
5 Citations
Methods Citations
2

Figures and Tables from this paper

5 Citations

The Barycentric Lagrange Interpolation via Maclaurin Polynomials for Solving the Second Kind Volterra Integral Equations

  • E. S. ShoukrallaB. Ahmed
  • 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.

The Use of Lavrentiev Regularization Method in Fredholm Integral Equations of the First Kind

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…

Non-polynomial spline functions and Quasi-linearization to approximate nonlinear Volterra integral equation

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…

Bézier interpolation improves the inference of dynamical models from data.

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.

Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations and Their Numerical Solutions

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…

References

SHOWING 1-10 OF 28 REFERENCES

Numerical Method for solving Volterra Integral Equations with a Convolution Kernel

This paper presents a numerical method for solving the Volterra integral equation with a convolution kernel. The integral equation was first converted to an algebraic equation using the Laplace…

Bernstein polynomials for solving Abel's integral equation

This paper presents a numerical method for solving Abel’s integral equation as singular Volterra integral equations. In the proposed method, the functions in Abel’s integral equation are approximated…

Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential…

Application of Legendre Polynomials in Solving Volterra Integral Equations of the Second Kind

A nu merical method is presented in this paper to solve linear Vo lterra integral equations of the second kind. In this proposed method, orthogonal Legendre polynomials are employed to approximate a…

Use of Bernstein Polynomials in Numerical Solutions of Volterra Integral Equations

In this paper the Bernstein polynomials are used to approximate the solutions of linear Volterra integral equations. Both second and first kind integral equations, with regular, as well as weakly…

Deriving Novel Formulas and Identities for the Bernstein Basis Functions and Their Generating Functions

By using the generating functions for the Bernstein basis functions, various functional equations, differential equations and second order partial differential equations are derived and new proofs of various identities, relations, integrals and derivatives are given.

A new approach to the numerical solution of Volterra integral equations by using Bernstein’s approximation

Numerical solution of nonlinear Volterra integral equations of the second kind by using Chebyshev polynomials

Numerical Solutions of Volterra Integral Equations Using Laguerre Polynomials

We solve numerically Volterra integral equations, of first and second kind with regular and singular kernels, by the well known Galerkin weighted residual method. For this, we derive a simple and…

Integral Equations and Their Applications

1 IntroductionPreliminary concept of the integral equation Historical background of the integral equation An illustration from mechanics Classification of integral equations Converting Volterra…