﻿ Solving Volterra Integral Equations of the Second Kind with Convolution ‎Kernel‎

# Solving Volterra Integral Equations of the Second Kind with Convolution ‎Kernel‎

##### نویسندگان
• A. R. Vahidi Department of Mathematics, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, ‎Iran.
• M. S. Barikbin Department of Mathematics, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.
• T. ِDamercheli Department of Mathematics, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, ‎Iran.
##### چکیده

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain the approximate solution of the second kind Volterra integral equations with convolution kernel and Maleknejad ‎et al. ‎[K. Maleknejad ‎and‎ T. Damercheli, Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the Taylor expansion method, ‎Indian J. Pure Appl. Math.‎ (2014)] ‎to gain the approximate solutions of systems of second kind Volterra integral equations with the help of Taylor expansion method. The Taylor expansion method transforms the integral equation into a linear ordinary differential equation (ODE) which, in this case, requires specified boundary conditions. Boundary conditions can be determined using the integration technique instead of differentiation technique. This method is more  stable than derivative method and can be implemented to obtain an approximate solution of the Volterra integral equation with smooth and weakly singular kernels. An error analysis for the method is provided. A comparison between our obtained results and the previous results is made which shows that the suggested method is accurate enough and more ‎stable.‎

برای دانلود باید عضویت طلایی داشته باشید

برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

## The solving linear one-dimemsional Volterra integral equations of the second kind in reproducing kernel space

In this paper, to solve a linear one-dimensional Volterra  integral equation of the second kind. For this purpose using the equation form, we have defined a linear transformation and by using it's conjugate and reproducing kernel functions, we obtain a basis for the functions space.Then we obtain the solution of  integral equation in terms of the basis functions. The examples presented in this ...

متن کامل

## Solving Second Kind Volterra-Fredholm Integral Equations by Using Triangular Functions (TF) and Dynamical Systems

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)‎. ‎The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system‎. ‎In this article‎, ‎the obtained nonlinear system has been solved as a dynamical system‎. ‎The solution of the obtained nonlinear system by the dynamical system throug...

متن کامل

## A Fast and Accurate Expansion-Iterative Method for Solving Second Kind Volterra Integral Equations

This article proposes a fast and accurate expansion-iterative method for solving second kind linear Volterra integral equations. The method is based on a special representation of vector forms of triangular functions (TFs) and their operational matrix of integration. By using this approach, solving the integral equation reduces to solve a recurrence relation. The approximate solution of integra...

متن کامل

## Kernel perturbations for convolution first kind Volterra integral equations

Because of their causal structure, (convolution) Volterra integral equations arise as models in a variety of real-world situations including rheological stress-strain analysis, population dynamics and insurance risk prediction. In such practical situations, often only an approximation for the kernel is available. Consequently, a key aspect in the analysis of such equations is estimating the eff...

متن کامل

## Negative norm error control for second-kind convolution Volterra equations

We consider a piecewise constant nite element approximation to the convolution Volterra equation problem of the second kind: nd u such that u = f + u in a time interval 0; T ]. An a posteriori estimate of the error measured in the W ?1 p (0; T) norm is developed and used to provide a time step selection criterion for an adaptive solution algorithm. Numerical examples are given for problems in w...

متن کامل

## Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

متن کامل

ذخیره در منابع من

ذخیره شده در منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی راحت تر خواهید کرد

دانلود متن کامل برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره 13  شماره 1

صفحات  63- 69

تاریخ انتشار 2021-09-01

{@ msg @}

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

کلمات کلیدی

میزبانی شده توسط پلتفرم ابری doprax.com