Extension of Iteration Method for Determining Strain Distributions to the Uniformly Stressed Plate With a Hole

1963 ◽  
Vol 30 (2) ◽  
pp. 210-214 ◽  
Author(s):  
E. A. Davis
Keyword(s):  
Iterative Method ◽  
Strain Hardening ◽  
Iteration Method ◽  
Incompressible Materials

The iterative method for determining strain distributions is applied to a uniformly stressed plate with a hole at the center. The method is not limited to incompressible materials; the load can be raised in incremental amounts; and strain-hardening of the material can be taken into consideration.

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

scholarly journals A Preconditioned Iteration Method for Solving Sylvester Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jituan Zhou ◽  
Ruirui Wang ◽  
Qiang Niu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Newton's Iteration ◽  
Gradient Based ◽  
Selection Of

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as a generalization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.

scholarly journals Heron’s cubic root iteration method with a new approach

2021 ◽  
Author(s):  
S. Gadtia ◽  
S. K. Padhan
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Interpolation Formula ◽  
Alternative Proof ◽  
New Approach ◽  
Iteration Formula ◽  
Odd Order ◽  
Even Order ◽  
Lagrange’S Method

Abstract Heron’s cubic root iteration formula conjectured by Wertheim is proved and extended for any odd order roots. Some possible proofs are suggested for the roots of even order. An alternative proof of Heron’s general cubic root iterative method is explained. Further, Lagrange’s interpolation formula for nth root of a number is studied and found that Al-Samawal’s and Lagrange’s method are equivalent. Again, counterexamples are discussed to justify the effectiveness of the present investigations.

scholarly journals Some conditions for convergence of the method of iterations for solving a nonlinear equation

2018 ◽  
Author(s):  
Н.И. Федоренко
Keyword(s):  
Nonlinear Equation ◽  
Iterative Method ◽  
Nonlinear Equations ◽  
Mathematical Expectation ◽  
Iteration Method ◽  
Branching Process ◽  
Branching Processes ◽  
Type A ◽  
Majorant Condition

Одной из трудностей, возникающих в связи с использованием ветвящихся процессов для решения нелинейных уравнений является выполнение так называемых мажорантных условий, ответственных за существование и конечность математического ожидания оценок, построенных на траекториях ветвящегося процесса. Вопрос выполнения мажорантного условия тесно связан со сходимостью итерационного метода. В статье рассматриваются некоторые утверждения о сходимости метода итераций для решения нелинейного уравнения одного вида. На примере устанавливается меньшая ограничительность мажорантного условия, соответствующего полученным утверждениям. One of the difficulties arising in connection with the use of branching processes for solving nonlinear equations is the fulfillment of the so-called majorant conditions responsible for the existence and finiteness of the mathematical expectation of estimates built on the trajectories of the branching process. The question of the fulfillment of the majorant condition related to the convergence of the iterative method. The article discusses some of the statements about the convergence of the iteration method for solving a nonlinear equation of the definite type. A less restrictive majorant condition is established on the example.

Application of Accelerated Iterative Method in Calculating Wave Length in Harbor Engineering

2011 ◽  
Vol 130-134 ◽  
pp. 3481-3484
Author(s):  
Shou Jun Wang ◽  
Ming Wei Wei
Keyword(s):  
Iterative Method ◽  
Calculation Method ◽  
Iteration Method ◽  
Wave Length ◽  
Newton Iteration ◽  
Convergence Speed ◽  
Iteration Formula ◽  
Convergence Results ◽  
Computing Speed

In this paper, a specific application accelerated iterative method is presented for calculating wave length in harbor engineering, which includes calculation method of wave length and specific implement in Excel. Different wavelengths into the iteration formula to calculate the same result can be obtained, but the calculation speed of different methods have significant differences to arrive at the fastest method . Calculated by accelerating the iteration method can significantly increase the computing speed and calculation steps. After the derivation of several methods and calculations show that Newton iteration is the fastest way to convergence speed, in the practical range of about 10 steps through the iterative convergence results can be obtained.

Simple iteration method for structural static reanalysis

2009 ◽  
Vol 36 (9) ◽  
pp. 1535-1538 ◽  
Author(s):  
Haifeng Liu ◽  
Baisheng Wu ◽  
Zhengguang Li
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Stiffness Matrix ◽  
Potential Energy Function ◽  
Relaxation Parameter ◽  
Computational Time ◽  
Acceleration Technique ◽  
Structural Static Reanalysis ◽  
Finite Element Systems

This paper presents a simple iterative method for structural static reanalysis. A preconditioned Richardson’s iterative method is developed and the relaxation parameter is determined by a very simple formula derived from the corresponding potential energy function. Based on the iteration method, an acceleration technique is also established. The proposed method is intended to utilize the existing stiffness matrix factorization completed for the initial design, require matrix-by-vector products only, preserve the ease of implementation and improve significantly the quality of the results. The method is suitable for general finite element systems. Calculation of derivatives is not required. The computational time is considerably reduced. A numerical example is used to validate the effectiveness of the proposed reanalysis method.

Research on Iterative Method in Solving Linear Equations on the Hadoop Platform

2013 ◽  
Vol 347-350 ◽  
pp. 2763-2768
Author(s):  
Yi Di Liu
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Linear Equations ◽  
Engineering Problems ◽  
Jacobi Iteration ◽  
Hadoop Platform ◽  
Iteration Methods ◽  
Division Operation

Solving linear equations is ubiquitous in many engineering problems, and iterative method is an efficient way to solve this question. In this paper, we propose a general iteration method for solving linear equations. Our general iteration method doesnt contain denominators in its iterative formula, and this relaxes the limits that traditional iteration methods require the coefficient aii to be non-zero. Moreover, as there is no division operation, this method is more efficient. We implement this method on the Hadoop platform, and compare it with the Jacobi iteration, the Guass-Seidel iteration and the SOR iteration. Experiments show that our proposed general iteration method is not only more efficient, but also has a good scalability.

scholarly journals An Iterative Method for Solving Quadratic Optimal Control Problem Using Scaling Boubaker Polynomials

2020 ◽  
Vol 5 (2) ◽  
Author(s):  
Imad Noah Ahmed ◽  
Eman Hassan Ouda
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Iterative Method ◽  
Control Problem ◽  
Iteration Method ◽  
Numerical Examples ◽  
Boubaker Polynomials ◽  
Quadratic Optimal Control

  Abstract     In this paper, an iteration method was used for solving a quadratic optimal control problem (QOCP) by the aid of state parameterization technique and scaling Boubaker polynomials. Some numerical examples were added to show the applicability of the method, also a comparison with other method was presented. The process steps were illustrated by some numerical examples with graphs done by Matlab.

scholarly journals A new iteration method for the solution of third-order BVP via Green's function

2021 ◽  
Vol 54 (1) ◽  
pp. 425-435
Author(s):  
Fatma Aydın Akgun ◽  
Zaur Rasulov
Keyword(s):  
Iterative Method ◽  
Green’S Function ◽  
Green's Function ◽  
Iteration Method ◽  
Existence And Uniqueness ◽  
Necessary Conditions ◽  
Uniqueness Theorems ◽  
Exact Results ◽  
Third Order ◽  
New Iterative Method

Abstract In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.

scholarly journals PHSS Iterative Method for Solving Generalized Lyapunov Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 38 ◽  
Author(s):  
Shi-Yu Li ◽  
Hai-Long Shen ◽  
Xin-Hui Shao
Keyword(s):  
Iterative Method ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Lyapunov Equation ◽  
New Method ◽  
New Methods ◽  
Generalized Lyapunov Equation ◽  
Improvement Effect ◽  
Hss Iteration ◽  
Hss Iteration Method

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

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