LINEAR INTEGRAL VOLTERRA EQUATION OF THE FIRST KIND IN THE BANACH SPACE

2015 ◽  
Vol 4 (2) ◽  
pp. 8-13
Author(s):  
Зенина ◽  
V. Zenina ◽  
Сапронов ◽  
Ivan Sapronov ◽  
Уточкина ◽  
...  
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Volterra Integral Equation ◽  
Volterra Equation ◽  
Polynomial Kernel ◽  
Integral Volterra Equation ◽  
Integrable Functions ◽  
Linear Integral ◽  
Space Of Integrable Functions

We construct solutions to a singular Volterra integral equation of the first kind with а polynomial kernel in the space of integrable functions whose values be-long to a Banach space.

Linear integral volterra equation of the first kind in the banach space

10.12737/4716 ◽  
2014 ◽  
Vol 2 (4) ◽  
pp. 113-114
Author(s):  
I. Sapronov ◽  
P. Zyukin ◽  
V. Zenina
Keyword(s):  
Banach Space ◽  
Volterra Equation ◽  
Integral Volterra Equation ◽  
Linear Integral

scholarly journals Nonlinear Volterra Integral Equation of the Second Kind and Biorthogonal Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
M. I. Berenguer ◽  
D. Gámez ◽  
A. I. Garralda-Guillem ◽  
M. C. Serrano Pérez
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Volterra Integral Equation ◽  
Biorthogonal System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Volterra Integral Equation ◽  
Numerical Resolution

We obtain an approximation of the solution of the nonlinear Volterra integral equation of the second kind, by means of a new method for its numerical resolution. The main tools used to establish it are the properties of a biorthogonal system in a Banach space and the Banach fixed point theorem.

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

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3947-3956 ◽  
Author(s):  
Kh. Maleknejad ◽  
J. Rashidinia ◽  
H. Jalilian
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Nonlinear Integral Equation ◽  
Linearization Method ◽  
Polynomial Spline ◽  
Linear Integral Equation ◽  
Spline Functions ◽  
Nonlinear Volterra Integral Equation ◽  
Spline Basis ◽  
Linear Integral

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 employed in nonlinear integral equation we obtain a linear integral equation then by using the Non-polynomial spline functions and collocation method the solution of the integral equation can be approximated. Analysis of convergence is investigated. At the end, some numerical examples are presented to show the effectiveness of the method.

scholarly journals On a Fredholm-Volterra integral equation

2021 ◽  
Vol 66 (3) ◽  
pp. 567-573
Author(s):  
Alexandru-Darius Filip ◽  
Ioan A. Rus
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Unique Solution ◽  
Iterative Algorithm ◽  
Volterra Integral Equation ◽  
Complex Banach Space

"In this paper we give conditions in which the integral equation $$x(t)=\displaystyle\int_a^c K(t,s,x(s))ds+\int_a^t H(t,s,x(s))ds+g(t),\ t\in [a,b],$$ where $a<c<b$, $K\in C([a,b]\times [a,c]\times \mathbb{B},\mathbb{B})$, $H\in C([a,b]\times [a,b]\times \mathbb{B},\mathbb{B})$, $g\in C([a,b],\mathbb{B})$, with $\mathbb{B}$ a (real or complex) Banach space, has a unique solution in $C([a,b],\mathbb{B})$. An iterative algorithm for this equation is also given."

A multiparametric family of solutions to a singular Volterra integral equation in a Banach space

2011 ◽  
Vol 55 (1) ◽  
pp. 50-61
Author(s):  
I. V. Sapronov
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Volterra Integral Equation

scholarly journals On the structure of the set of solutions of a Volterra integral equation in a Banach space

1994 ◽  
Vol 59 (1) ◽  
pp. 33-39
Author(s):  
Krzysztof Czarnowski
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Volterra Integral Equation

scholarly journals Interpolation rational integral fraction of nth order on a continuum set of nodes

2021 ◽  
pp. 101-105
Author(s):  
Ihor Demkiv ◽  
Yaroslav Baranetskyi ◽  
Halyna Berehova
Keyword(s):  
Integral Equation ◽  
Volterra Equation ◽  
Standard Form ◽  
Integral Volterra Equation ◽  
Substitution Rule ◽  
Rational Integral

The paper constructs and investigates an integral rational interpolant of the nth order on a continuum set of nodes, which is the ratio of a functional polynomial of the first degree to a functional polynomial of the (n-1)th degree. Subintegral kernels are determined from the corresponding continuum conditions. Additionally, we obtain an integral equation to determine the kernel of the numerator integral. This integral equation, using elementary transformations, is reduced to the standard form of the integral Volterra equation of the second kind. Substituting the obtained solution into expressions for the rest of the kernels, we obtain expressions for all kernels included in the integral rational interpolant. Then, in order for a rational functional of the nth order to be interpolation on continuous nodes, it is sufficient for this functional to satisfy the substitution rule. Note that the resulting interpolant preserves any rational functional of the obtained form.

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