scholarly journals Picard Successive Approximation Method for Solving Differential Equations Arising in Fractal Heat Transfer with Local Fractional Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ai-Min Yang ◽  
Cheng Zhang ◽  
Hossein Jafari ◽  
Carlo Cattani ◽  
Ying Jiao
Keyword(s):  
Successive Approximation ◽  
Approximation Method ◽  
Present Method ◽  
Flux Distribution ◽  
Approximate Solutions ◽  
Successive Approximation Method ◽  
Fourier Law ◽  
One Dimensional ◽  
Fractal Media ◽  
The Given

The Fourier law of one-dimensional heat conduction equation in fractal media is investigated in this paper. An approximate solution to one-dimensional local fractional Volterra integral equation of the second kind, which is derived from the transformation of Fourier flux equation in discontinuous media, is considered. The Picard successive approximation method is applied to solve the temperature field based on the given Mittag-Leffler-type Fourier flux distribution in fractal media. The nondifferential approximate solutions are given to show the efficiency of the present method.

scholarly journals On the convergence of a coupling successive approximation method for solving Duffing equation

2014 ◽  
Vol 36 (3) ◽  
pp. 185-200
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solutions ◽  
Successive Approximation ◽  
Approximation Method ◽  
Approximate Solutions ◽  
Duffing Equation ◽  
Successive Approximation Method ◽  
Third Order ◽  
Duffing Equations ◽  
Small Parameters

General Duffing equations occur in many problems of Mechanics and Dynamics. These equations include nonlinear terms of second and third order, their coefficients are finite but not small parameters. For finding analytical approximate solutions of the general Duffing equation the coupling successive approximation method (CSAM) has been proposed by the authors.In the present paper the convergence of mentioned method is proven and a condition relating coefficients of Duffing equation to provide the convergence procedure is formulated. Emphasize that the assumption of small parameters is not used in the proving.Some examples are presented to illustrate the proposed method, particularly exact solutions of some problems are compared with analytical approximate ones found by CSAM.

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 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.

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.

Sign in / Sign up

Export Citation Format

Share Document