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Lucas polynomials for solving linear integral equations

Nadir M.

Journal of Theoretical and Applied Computer Science

2017

Vol. 11, nr 1

13--19

In this work, we seek the approximate solution of Fredholm and Volterra integral equations using Lucas polynomials and a given test functions, in order to reduce those equations to a linear system where its solution is to find the Lucas coefficients and thereafter the solution of the equation.The convergence of this method is assured and the error is compared with other methods.

Homotopy approach for solving two-dimensional integral equations of the second kind

Hetmaniok E., Nowak I., Słota D., Zielonka A.

Computer Assisted Methods in Engineering and Science

2016

Vol. 23, no. 1

19--41

In this paper, the two-dimensional linear and nonlinear integral equations of the second kind is analyzed. The homotopy analysis method (HAM) is used for determining the solution of the investigated equation. In this method, a solution is sought in the series form. It is shown that if this series is convergent, its sum gives the solution of the considered equation. The sufficient condition for the convergence of the series is also presented. Additionally, the error of approximate solution, obtained as partial sum of the series, is estimated. Application of the HAM is illustrated by examples.

A variational form with Bernoulli series for linear integral equations

Nadir M.

Journal of Theoretical and Applied Computer Science

2014

Vol. 8, nr 3

31--36

In this work, we seek the approximate solution of Fredholm integral equations by truncation Bernoulli series approximation using a variational form for the equation. This one is reduced to a linear system where the solution of this latter gives the Bernoulli coefficients and thereafter the solution of the equation.The convergence and the error analysis of this method are discussed. Finally, we compare our numerical results by others.

Linear Fredholm integral equations and the integral of Kurzweil

Federson M., Bianconi R.

Journal of Applied Analysis

2002

Vol. 8, nr 1

83-110

We apply the Kurzweil-Henstock integral setting to prove a Predholm Alternative-type result for the integral equation x(t)-K ∫[a,b] α(t,s) x (s)ds = f (t), t∈[a,b], J[a,b) where x and f are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval [a, b] of the real line with values on Banach spaces. An application is given.