Integral equations
1. An efficient method for the numerical solution of functional integral equations

M. Nili Ahmadabadi

Volume 09, Issue 02 , Spring 2020, , Pages 105-111

Abstract
  We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained.  Read More

Integral equations
2. New iteration process for approximating fixed points in Banach spaces

J. D. Bhutia; K. Tiwary

Volume 08, Issue 04 , Autumn 2019, , Pages 237-250

Abstract
  ‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized ...  Read More

Integral equations
3. Hyers–Ulam–Rassias stability of impulsive Volterra integral equation via a fixed point approach

R. Shah; A. Zada

Volume 08, Issue 04 , Autumn 2019, , Pages 219-227

Abstract
  ‎In this paper‎, ‎we establish the Hyers--Ulam--Rassias stability and the Hyers--Ulam stability of impulsive Volterra integral equation by using a fixed point method‎.  Read More

Integral equations
4. Numerical solution of a type of weakly singular nonlinear Volterra integral equation by Tau Method

H. Laeli Dastjerdi; M. Nili Ahmadabadi

Volume 07, Issue 02 , Spring 2018, , Pages 75-85

Abstract
  ‎In this paper‎, ‎a matrix based method is considered for the solution of a class of nonlinear Volterra integral equations with a kernel of the general form $s^{\beta}(t-s)^{-\alpha}G(y(s))$ based on the Tau method‎. ‎In this method‎, ‎a transformation of the independent variable ...  Read More

Integral equations
5. Random fixed point theorems with an application to a random nonlinear integral equation

R. A. Rashwan; H. A. Hammad

Volume 05, Issue 02 , Spring 2016, , Pages 119-133

Abstract
  In this paper, stochastic generalizations of some fixed point for operators satisfying random contractively generalized hybrid and some other contractive condition have been proved. We discuss also the existence of a solution to a nonlinear random integral equation in Banah spaces.  Read More

Integral equations
6. A numerical solution of mixed Volterra Fredholm integral equations of Urysohn type on non-rectangular regions using meshless methods

M. Nili Ahmadabadi; H. Laeli Dastjerdi

Volume 04, Issue 04 , Autumn 2015, , Pages 289-304

Abstract
  In this paper, we propose a new numerical method for solution of Urysohn two dimensional mixed Volterra-Fredholm integral equations of the second kind on a non-rectangular domain. The method approximates the solution by the discrete collocation method based on inverse multiquadric radial basis functions ...  Read More

Integral equations
7. Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

M. Matinfar; A. Riahifar

Volume 04, Issue 03 , Summer 2015, , Pages 217-228

Abstract
  In this work, we conduct a comparative study among the combine Laplace transform and modi ed Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear ...  Read More

Integral equations
8. Bernoulli collocation method with residual correction for solving integral-algebraic equations

F. Mirzaee

Volume 04, Issue 03 , Summer 2015, , Pages 193-208

Abstract
  The principal aim of this paper is to serve the numerical solution of an integral-algebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its ...  Read More

Integral equations
9. Numerical solution of Fredholm integral-differential equations on unbounded domain

M. Matinfar; A. Riahifar

Volume 04, Issue 01 , Winter 2015, , Pages 43-52

Abstract
  In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties ...  Read More

Integral equations
10. Expansion methods for solving integral equations with multiple time lags using Bernstein polynomial of the second kind

M. Paripour; Z. Shojaei; S. Abdolahi

Volume 03, Issue 01 , Winter 2014, , Pages 35-45

Abstract
  In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical ...  Read More