Two-Level Newton Iterative Method for the 2D/3D Stationary Incompressible Magnetohydrodynamics

2014 ◽  
Vol 63 (2) ◽  
pp. 426-451 ◽  
Author(s):  
Xiaojing Dong ◽  
Yinnian He
Keyword(s):  
Iterative Method ◽  
Newton Iterative Method ◽  
Stationary Incompressible Magnetohydrodynamics ◽  
Incompressible Magnetohydrodynamics

The Oseen Type Finite Element Iterative Method for the Stationary Incompressible Magnetohydrodynamics

2017 ◽  
Vol 9 (4) ◽  
pp. 775-794 ◽  
Author(s):  
Xiaojing Dong ◽  
Yinnian He
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Iterative Method ◽  
Mesh Size ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Stability And Convergence ◽  
Stationary Incompressible Magnetohydrodynamics ◽  
Image Position ◽  
Incompressible Magnetohydrodynamics

AbstractIn this article, by applying the Stokes projection and an orthogonal projection with respect to curl and div operators, some new error estimates of finite element method (FEM) for the stationary incompressible magnetohydrodynamics (MHD) are obtained. To our knowledge, it is the first time to establish the error bounds which are explicitly dependent on the Reynolds numbers, coupling number and mesh size. On the other hand, The uniform stability and convergence of an Oseen type finite element iterative method for MHD with respect to high hydrodynamic Reynolds number Re and magnetic Reynolds number Rm, or small δ=1–σ with(C0, C1 are constants depending only on Ω and F is related to the source terms of equations) are analyzed under the condition that . Finally, some numerical tests are presented to demonstrate the effectiveness of this algorithm.

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Research on Newton Iterative Method and its Application in Locating Problem of Cameras

2010 ◽  
Vol 108-111 ◽  
pp. 112-116
Author(s):  
Ai Min Yang ◽  
Jin Cai Chang ◽  
Shao Hong Yan
Keyword(s):  
Iterative Method ◽  
Plane Surface ◽  
Target Surface ◽  
Newton Iterative Method ◽  
Limited Condition ◽  
Surface Length

According to the imagery coordinate’s mapping relation between the three points’(A,C,E) geometric limited condition on target surface ( length, perpendicular) and the image’s coordinate on the imagery plane surface to construct non- lineable equation models, we make use of the method of abstracting the center of a circle to get the coordinates of the three points 、 、 .In order to improve the precision and decrease the quantity of operation, we take the accelerateNewton Newton iterative method to evaluate the original numerical value by adding its repeating times to increase the precision of model, then to solve out the numerical value of coordinates of the three points A,C,E on the target’s surface, on the basis of this numerical value, we can fix the solution of the target’s surface’s equation. Try to assure the precision of the constructed model through these erroneous values, meanwhile, to make out the concrete analysis about the model’s stability.

scholarly journals Some novel Newton-type methods for solving nonlinear equations

2019 ◽  
Vol 38 (3) ◽  
pp. 111-123
Author(s):  
Morteza Bisheh-Niasar ◽  
Abbas Saadatmandi
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Basins Of Attraction ◽  
Sixth Order ◽  
New Method ◽  
Order Convergence ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Newton Iterative Method

The aim of this paper is to present a new nonstandard Newton iterative method for solving nonlinear equations. The convergence of the proposed method is proved and it is shown that the new method has cubic convergence. Furthermore, two new multi-point methods with sixth-order convergence, based on the introduced method, are presented. Also, we describe the basins of attraction for these methods. Finally, some numerical examples are given to show the performance of our methods by comparing with some other methods available in the literature

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