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.

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 Application of the successive approximation method to the analysis of bending plates

2018 ◽  
Vol 251 ◽  
pp. 04058
Author(s):  
Radek Gabbasov ◽  
Vladimir Filatov ◽  
Nikita Ryasny
Keyword(s):  
Boundary Conditions ◽  
Successive Approximation ◽  
Approximation Method ◽  
High Accuracy ◽  
Numerical Results ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Successive Approximation Method ◽  
Medium Thickness ◽  
Bending Plates

This work presents an algorithm for calculating the bending plates of medium thickness according to the Reissner’. To obtain numerical results, the method of successive approximations (MSA) is used. This method has high accuracy and fast convergence, which was confirmed by the solution of a range of tasks. Publication of the results of the calculation of plates of medium thickness with the boundary conditions revised here is supposed to be in the following articles.

Deconvolution by successive approximations

Geophysics ◽  
1982 ◽  
Vol 47 (12) ◽  
pp. 1724-1730 ◽  
Author(s):  
Lucien J. B. LaCoste
Keyword(s):  
Successive Approximation ◽  
Approximation Method ◽  
Time Domain ◽  
Simple Procedure ◽  
Successive Approximations ◽  
Successive Approximation Method ◽  
The Time Domain

Although various methods of deconvolution have been known for many years, they are not generally regarded as being routinely usable. The successive approximation method described in this article should be an improvement in that respect. It operates in the time domain and is based on a simple procedure. I first discuss the mathematics involved and then give some examples to illustrate how the method works and some of the things it can do.

scholarly journals Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

scholarly journals A multistage successive approximation method for Riccati differential equations

2021 ◽  
Vol 10 (3) ◽  
Author(s):  
Petrus Setyo Prabowo ◽  
Sudi Mungkasi
Keyword(s):  
Differential Equations ◽  
Successive Approximation ◽  
Systems Engineering ◽  
Approximation Method ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Theory And Practice ◽  
Successive Approximation Method ◽  
Riccati Differential Equations ◽  
Variational Iteration

Riccati differential equations have played important roles in the theory and practice of control systems engineering. Our goal in this paper is to propose a new multistage successive approximation method for solving Riccati differential equations. The multistage successive approximation method is derived from an existing piecewise variational iteration method for solving Riccati differential equations. The multistage successive approximation method is simpler in terms of computing implementation in comparison with the existing piecewise variational iteration method. Computational tests show that the order of accuracy of the multistage successive approximation method can be made higher by simply taking more number of successive iterations in the multistage evolution. Furthermore, taking small size of each subinterval and taking large number of iterations in the multistage evolution lead that our proposed method produces small error and becomes high order accurate.

NON-LIPSCHITZ STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTI-PARAMETER BROWNIAN MOTIONS

2006 ◽  
Vol 06 (03) ◽  
pp. 329-340 ◽  
Author(s):  
XICHENG ZHANG ◽  
JINGYANG ZHU
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Lebesgue Measure ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Gronwall’S Inequality

By proving an extension of nonlinear Bihari's inequality (including Gronwall's inequality) to multi-parameter and non-Lebesgue measure, in this paper we first prove by successive approximation the existence and uniqueness of solution of stochastic differential equation with non-Lipschitz coefficients and driven by multi-parameter Brownian motion. Then we study two discretizing schemes for this type of equation, and obtain their L2-convergence speeds.

SUCCESSIVE APPROXIMATIONS OF INFINITE DIMENSIONAL SDES WITH JUMP

2005 ◽  
Vol 05 (04) ◽  
pp. 609-619 ◽  
Author(s):  
GUILAN CAO ◽  
KAI HE ◽  
XICHENG ZHANG
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Successive Approximations ◽  
Uniqueness Of Solutions ◽  
Infinite Dimensional

In this paper, we study the existence and uniqueness of solutions to non-Markovian stochastic differential equations with jump and non-Lipschitz coefficients in infinite dimensional spaces by successive approximation.

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