Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: nieliniowe równania całkowe

Sortuj według:

Ogranicz wyniki do:

Computation of solution of integral equations via fixed point results

Alqudah Manar A., Garodia Chanchal, Uddin Izhar, Nieto Juan J.

Demonstratio Mathematica

2022

Vol. 55, nr 1

772--785

The motive of this article is to study a modified iteration scheme for monotone nonexpansive mappings in the class of uniformly convex Banach space and establish some convergence results. We obtain weak and strong convergence results. In addition, we present a nontrivial numerical example to show the convergence of our iteration scheme. To demonstrate the utility of our scheme, we discuss the solution of nonlinear integral equations as an application, which is again supported by a nontrivial example.

Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method

Georgieva Atanaska

Demonstratio Mathematica

2021

Vol. 54, nr 1

11--24

The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.

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.