Estimates of a Stabilization Rate as 𝑡 → ∞ Solutions of a Nonlinear Integro-Differential Equation

2002 ◽  
Vol 9 (1) ◽  
pp. 57-70
Author(s):  
T. Jangveladze ◽  
Z. Kiguradze
Keyword(s):  
Differential Equation ◽  
Electromagnetic Field ◽  
Asymptotic Behavior ◽  
Integro Differential Equation

Abstract The asymptotic behavior as 𝑡 → ∞ of solutions of a nonlinear integro-differential equation is studied. The equation arises as a model describing the penetration of the electromagnetic field in to a substance.

scholarly journals The Asymptotic Behavior of Solutions of a Fractional Integro-differential Equation

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Integral Operator ◽  
Fractional Integral ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Power Functions ◽  
Initial Value ◽  
Integro Differential Equation ◽  
Underlying Space

In this paper, we study the asymptotic behavior of solutions for an initial value problem with a nonlinearfractional integro-differential equation. Most of the existing results in the literature assume the continuity of theinvolved kernel. We consider here a kernel that is not necessarily continuous, namely, the kernel of the RiemannLiouville fractional integral operator that might be singular. We determine certain sufficient conditions underwhich the solutions, in an appropriate underlying space, behave eventually like power functions. For this purpose,we establish and generalize some well-known integral inequalities with some crucial estimates. Our findings aresupported by examples and numerical calculations.

Averaged semi-discrete scheme of sum-approximation for one nonlinear multi-dimensional integro-differential parabolic equation

2020 ◽  
Vol 27 (3) ◽  
pp. 367-373
Author(s):  
Temur Jangveladze ◽  
Zurab Kiguradze
Keyword(s):  
Differential Equation ◽  
Electromagnetic Field ◽  
Parabolic Equation ◽  
Mathematical Simulation ◽  
Parabolic Type ◽  
Integro Differential Equation ◽  
Discrete Scheme ◽  
Maxwell’S System ◽  
Field Penetration

AbstractThe paper is devoted to the construction and study of the additive averaged semi-discrete scheme for one nonlinear multi-dimensional integro-differential equation of parabolic type. The studied equation is based on the well-known Maxwell’s system arising in mathematical simulation of electromagnetic field penetration into a substance.

Some numerical graphs with successive approximation method of fractional integro–differential equation

2019 ◽  
Vol 8 (4) ◽  
pp. 36
Author(s):  
Samir H. Abbas
Keyword(s):  
Differential Equation ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximation Method ◽  
Integro Differential Equation

This paper studies the existence and uniqueness solution of fractional integro-differential equation, by using some numerical graphs with successive approximation method of fractional integro –differential equation. The results of written new program in Mat-Lab show that the method is very interested and efficient. Also we extend the results of Butris [3].

Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

2018 ◽  
pp. 491
Author(s):  
Abdul Khaleq O. Al-Jubory ◽  
Shaymaa Hussain Salih
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear System ◽  
Differential Equations ◽  
Bernstein Basis ◽  
Traditional Methods ◽  
Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations  nonhomogeneous  of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.   

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