Solutions for an Integral-Differential Equation

2009 ◽  
pp. 703-712
Author(s):  
Nikos E. Mastorakis ◽  
Olga Martin
Keyword(s):  
Differential Equation ◽  
Integral Differential Equation

scholarly journals Numerical Algorithm to Solve a Class of Variable Order Fractional Integral-Differential Equation Based on Chebyshev Polynomials

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Kangwen Sun ◽  
Ming Zhu
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Numerical Algorithm ◽  
Chebyshev Polynomials ◽  
Fractional Integral ◽  
Numerical Solutions ◽  
Variable Order ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Integral Differential Equation

The purpose of this paper is to study the Chebyshev polynomials for the solution of a class of variable order fractional integral-differential equation. The properties of Chebyshev polynomials together with the four kinds of operational matrixes of Chebyshev polynomials are used to reduce the problem to the solution of a system of algebraic equations. By solving the algebraic equations, the numerical solutions are acquired. Further some numerical examples are shown to illustrate the accuracy and reliability of the proposed approach and the results have been compared with the exact solution.

scholarly journals A Note on the Stability of the Integral-Differential Equation of the Parabolic Type in a Banach Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Maksat Ashyraliyev
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Difference Scheme ◽  
Unique Solvability ◽  
Parabolic Type ◽  
Stability Estimates ◽  
The Difference ◽  
The Stability ◽  
Integral Differential Equation

The integral-differential equation of the parabolic type in a Banach space is considered. The unique solvability of this equation is established. The stability estimates for the solution of this equation are obtained. The difference scheme approximately solving this equation is presented. The stability estimates for the solution of this difference scheme are obtained.

scholarly journals Solution of an Integral-Differential Equation Arising in Oscillating Magnetic Fields Using Local Polynomial Regression

2014 ◽  
Vol 6 ◽  
pp. 101230 ◽  
Author(s):  
Fenglan Li ◽  
Tianshun Yan ◽  
Liyun Su
Keyword(s):  
Differential Equation ◽  
Magnetic Fields ◽  
Polynomial Regression ◽  
Regression Method ◽  
Computational Domain ◽  
Local Polynomial Regression ◽  
Local Polynomial ◽  
Time Periodic ◽  
Integral Differential Equation ◽  
Very High

An integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The local polynomial regression method (LPR) is used to solve this equation. The reliability of this method and the reduction in the size of computational domain give this method a wider applicability. Several representative examples are given to reconfirm the efficiency of these algorithms. The results of applying this theory to the integro-differential equation with time-periodic coefficients reveal that LPR method possesses very high accuracy, adaptability, and efficiency.

A Note on the Stability of the Integral-Differential Equation of the Parabolic Type

2011 ◽  
Author(s):  
Maksat Ashyraliyev ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Differential Equation ◽  
Parabolic Type ◽  
The Stability ◽  
Integral Differential Equation
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