Convergence of the Successive Approximation Method in the Cauchy Problem for an Integro-Differential Equation with Quadratic Nonlinearity

2019 ◽  
Vol 29 (2) ◽  
pp. 128-136 ◽  
Author(s):  
V. L. Vaskevich ◽  
A. I. Shcherbakov
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Successive Approximation ◽  
Approximation Method ◽  
Quadratic Nonlinearity ◽  
Successive Approximation Method ◽  
Integro Differential Equation ◽  
The Cauchy Problem

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].

scholarly journals Successive Approximation Method of Integro–Differential Equation With Applications

2019 ◽  
Vol 8 (3) ◽  
pp. 96
Author(s):  
Samir H. Abbas ◽  
Younis M. Younis
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Successive Approximation ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Successive Approximation Method ◽  
Integro Differential Equation

The aim of this paper is studying the existence and uniqueness solution of integro- differential equations by using Successive approximations method of picard. The results of written program in Mat-Lab show that the method is very interested and efficient with comparison the exact solution for solving of integro-differential equation.

scholarly journals Asymptotic Solutions of Scalar Integro-Differential Equations with Partial Derivatives and with Fast Oscillating Coefficients

2020 ◽  
Vol 13 (2) ◽  
pp. 287-302
Author(s):  
Burkhan Kalimbetov ◽  
Akisher Temirbekov ◽  
Abdimuhan Tolep
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Differential Equations ◽  
Unique Solvability ◽  
Regularization Method ◽  
Singularly Perturbed ◽  
Integral Term ◽  
Integro Differential Equation ◽  
The Cauchy Problem ◽  
Oscillating Coefficients

In the paper, ideas of the Lomov regularization method are generalized to the Cauchy problem for a singularly perturbed partial integro-differential equation in the case when the integral term contains a rapidly varying kernel. Regularization of the problem is carried out, the normal and unique solvability of general iterative problems is proved.

scholarly journals Integro-differential equation with two times modifications

2011 ◽  
Vol 27 (2) ◽  
pp. 209-216
Author(s):  
VERONICA-ANA ILEA ◽  
◽  
DIANA OTROCOL ◽  
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Operator Theory ◽  
Step Method ◽  
Picard Operator ◽  
Integro Differential Equation ◽  
The Cauchy Problem ◽  
Weakly Picard Operator

We consider an integro-differential equation with two times modifications. Existence, uniqueness and monotony results of solution for the Cauchy problem are obtained using weakly Picard operator theory. In the last section we present a step method for this type of equation.

scholarly journals Problem of Determining a Multidimensional Kernel in One Parabolic Integro–differential Equation

2021 ◽  
pp. 117-127
Author(s):  
Durdimurod K. Durdiev ◽  
Zhavlon Z. Nuriddinov
Keyword(s):  
Differential Equation ◽  
Inverse Problem ◽  
Cauchy Problem ◽  
Direct Problem ◽  
Contractive Mapping ◽  
Equivalent System ◽  
Direct And Inverse Problems ◽  
Integro Differential Equation ◽  
The Cauchy Problem ◽  
The Right

The multidimensional parabolic integro-differential equation with the time-convolution in- tegral on the right side is considered. The direct problem is represented by the Cauchy problem for this equation. In this paper it is studied the inverse problem consisting in finding of a time and spatial dependent kernel of the integrated member on known in a hyperplane xn = 0 for t > 0 to the solution of direct problem. With use of the resolvent of kernel this problem is reduced to the investigation of more convenient inverse problem. The last problem is replaced with the equivalent system of the integral equations with respect to unknown functions and on the bases of contractive mapping principle it is proved the unique solvability to the direct and inverse problems

4.—A Cauchy Problem for an Ordinary Integro-differential Equation

1974 ◽  
Vol 72 (1) ◽  
pp. 39-55 ◽  
Author(s):  
E. A. Catchpole
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Cauchy Problem ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Integro Differential Equation ◽  
Linearly Independent ◽  
The Cauchy Problem ◽  
Integral Equation Approach ◽  
Necessary And Sufficient

SynopsisIn this paper we study an ordinary second-order integro-differential equation (IDE) on a finite closed interval. We demonstrate the equivalence of this equation to a certain integral equation, and deduce that the homogeneous IDE may have either 2 or 3 linearly independent solutions, depending on the value of a parameter λ. We study a Cauchy problem for the IDE, both by this integral equation approach and by an independent approach, based on the perturbation theory for linear operators. We give necessary and sufficient conditions for the Cauchy problem to be solvable for arbitrary right-hand sides—these conditions again depend on λ—and specify the behaviour of the IDE when these conditions are not satisfied. At the end of the paper some examples are given of the type of behaviour described.

scholarly journals Ulam-Hyers Stability and Ulam-Hyers-Rassias Stability for Fuzzy Integrodifferential Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Nguyen Ngoc Phung ◽  
Bao Quoc Ta ◽  
Ho Vu
Keyword(s):  
Fixed Point ◽  
Successive Approximation ◽  
Integrodifferential Equation ◽  
Approximation Method ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Point Method ◽  
Successive Approximation Method ◽  
Rassias Stability

In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.

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