On some systems of convolution-type first-order integrodifferential equations on the semiaxis

2009 ◽  
Vol 61 (9) ◽  
pp. 1511-1528 ◽  
Author(s):  
A. Kh. Khachatryan ◽  
Kh. A. Khachatryan
Keyword(s):  
Integrodifferential Equations ◽  
Convolution Type ◽  
First Order

scholarly journals Periodic Boundary Value Problems for First-Order Impulsive Functional Integrodifferential Equations with Integral-Jump Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Chatthai Thaiprayoon ◽  
Decha Samana ◽  
Jessada Tariboon
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Jump Conditions ◽  
Comparison Result ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Minimal And Maximal Solutions

By developing a new comparison result and using the monotone iterative technique, we are able to obtain existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive functional integrodifferential equations with integral-jump conditions. An example is also given to illustrate our results.

scholarly journals Spin-Dependent Coupled Altarelli-Parisi Equations in the NLO and the Method of Successive Approximations

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Ranjit Choudhury ◽  
D. K. Choudhury
Keyword(s):  
Gluon Distribution ◽  
Quark Distribution ◽  
Distribution Functions ◽  
Integrodifferential Equations ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Leading Order ◽  
Order Linear ◽  
First Order ◽  
Analytic Expressions

The coupled Altarelli-Parisi (AP) equations for polarized singlet quark distribution and polarized gluon distribution, when considered in the small x limit of the next to leading order (NLO) splitting functions, reduce to a system of two first order linear nonhomogeneous integrodifferential equations. We have applied the method of successive approximations to obtain the solutions of these equations. We have applied the same method to obtain the approximate analytic expressions for spin-dependent quark distribution functions with individual flavour and polarized structure functions for nucleon.

scholarly journals Existence Results for the Nonlinear First Order Fuzzy Neutral Integrodifferential Equations

2013 ◽  
Vol 53 (1) ◽  
pp. 87-98
Author(s):  
Bheeman Radhakrishnan ◽  
Murugesan Nagarajan ◽  
Samayan Narayanamoorthy
Keyword(s):  
Existence Results ◽  
Integrodifferential Equations ◽  
First Order

scholarly journals Multiple Positive Solutions for First-Order Impulsive Integrodifferential Equations on the Half Line in Banach Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Dajun Guo
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Positive Solutions ◽  
Integrodifferential Equations ◽  
Half Line ◽  
Multiple Positive Solutions ◽  
First Order ◽  
The Fixed Point Theorem ◽  
Cone Expansion And Compression ◽  
Infinite Boundary Value Problem

The author discusses the multiple positive solutions for an infinite boundary value problem of first-order impulsive superlinear integrodifferential equations on the half line in a Banach space by means of the fixed point theorem of cone expansion and compression with norm type.

scholarly journals Iterative Splitting Methods for Integrodifferential Equations: Theory and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Jürgen Geiser
Keyword(s):  
Differential Equations ◽  
Splitting Methods ◽  
Integrodifferential Equations ◽  
Cauchy Problems ◽  
Splitting Schemes ◽  
Scattering Problems ◽  
First Order ◽  
Fast Solver ◽  
Transport Problems ◽  
Abstract Cauchy Problems

We present novel iterative splitting methods to solve integrodifferential equations. Such integrodifferential equations are applied, for example, in scattering problems of plasma simulations. We concentrate on a linearised integral part and a reformulation to a system of first order differential equations. Such modifications allow for applying standard iterative splitting schemes and for extending the schemes, respecting the integral operator. A numerical analysis is presented of the system of semidiscretised differential equations as abstract Cauchy problems. In the applications, we present benchmark and initial realistic applications to transport problems with scattering terms. We also discuss the benefits of such iterative schemes as fast solver methods.

scholarly journals Fast methods for the solution of singular integro-differential and differential equations

1981 ◽  
Vol 4 (4) ◽  
pp. 775-794
Author(s):  
L. F. Abd-Elal
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Integrodifferential Equations ◽  
Solution Time ◽  
First Order ◽  
Chebyshev Expansion ◽  
Fast Methods ◽  
The Galerkin Method

Uniform methods based on the use of the Galerkin method and different Chebyshev expansion sets are developed for the numerical solution of linear integrodifferential equations of the first order. These methods take a total solution time0(N2lnN)usingNexpansion functions, and also provide error extimates which are cheap to compute. These methods solve both singular and regular integro-differential equations. The methods are also used in solving differential equations.

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