Plane elasticity problems by barycentric rational interpolation collocation method and a regular domain method

2020 ◽  
Vol 121 (18) ◽  
pp. 4134-4156
Author(s):  
Meiling Zhuang ◽  
Changqing Miao ◽  
Siyuan Ji
Keyword(s):  
Collocation Method ◽  
Rational Interpolation ◽  
Plane Elasticity ◽  
Regular Domain ◽  
Domain Method ◽  
Elasticity Problems ◽  
Barycentric Rational Interpolation

scholarly journals The barycentric rational interpolation collocation method for boundary value problems

2018 ◽  
Vol 22 (4) ◽  
pp. 1773-1779 ◽  
Author(s):  
Dan Tian ◽  
Ji-Huan He
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Analytical Methods ◽  
Boundary Value ◽  
Rational Interpolation ◽  
Higher Order ◽  
Barycentric Rational Interpolation

Higher-order boundary value problems have been widely studied in thermal science, though there are some analytical methods available for such problems, the barycentric rational interpolation collocation method is proved in this paper to be the most effective as shown in three examples.

scholarly journals Linear Barycentric Rational Method for Solving Schrodinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Peichen Zhao ◽  
Yongling Cheng
Keyword(s):  
Schrödinger Equation ◽  
Convergence Rate ◽  
Collocation Method ◽  
Schrodinger Equation ◽  
Interpolation Method ◽  
Rational Interpolation ◽  
Barycentric Interpolation ◽  
Rational Polynomial ◽  
The Matrix ◽  
Barycentric Rational Interpolation

A linear barycentric rational collocation method (LBRCM) for solving Schrodinger equation (SDE) is proposed. According to the barycentric interpolation method (BIM) of rational polynomial and Chebyshev polynomial, the matrix form of the collocation method (CM) that is easy to program is obtained. The convergence rate of the LBRCM for solving the Schrodinger equation is proved from the convergence rate of linear barycentric rational interpolation. Finally, a numerical example verifies the correctness of the theoretical analysis.

scholarly journals Analysis for Irregular Thin Plate Bending Problems on Winkler Foundation by Regular Domain Collocation Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Meiling Zhuang ◽  
Changqing Miao
Keyword(s):  
Boundary Conditions ◽  
Thin Plate ◽  
Rational Interpolation ◽  
Winkler Foundation ◽  
Plate Bending ◽  
Rectangular Region ◽  
Regular Domain ◽  
Bending Problems ◽  
Thin Plate Bending ◽  
Barycentric Rational Interpolation

Regular domain collocation method based on barycentric rational interpolation for solving irregular thin plate bending problems on Winkler foundation is presented in this article. Embedding the irregular plate into a regular domain, the barycentric rational interpolation is used to approximate the unknown function. The governing equation and the boundary conditions of thin plate bending problems on Winkler foundation in a rectangular region can be discretized by the differentiation matrices of barycentric rational interpolation. The additional method or the substitute method is used to impose the boundary conditions. The overconstraint equations can be solved by using the least square method. Numerical solutions of bending deflection for the irregular plate bending problems on Winkler foundation are obtained by interpolating the data on rectangular region. Numerical examples illuminate that the proposed method for irregular thin plate bending problems on Winkler foundation has the merits of simple formulations, efficiency, and relative error precision of 10−9 orders of magnitude.

scholarly journals Linear Barycentric Rational Collocation Method for Beam Force Vibration Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jin Li ◽  
Yu Sang
Keyword(s):  
Convergence Rate ◽  
Collocation Method ◽  
Convergence Rates ◽  
Rational Interpolation ◽  
Vibration Equation ◽  
Numerical Examples ◽  
Space And Time ◽  
Force Vibration ◽  
The Matrix ◽  
Barycentric Rational Interpolation

The linear barycentric rational collocation method for beam force vibration equation is considered. The discrete beam force vibration equation is changed into the matrix forms. With the help of convergence rate of barycentric rational interpolation, both the convergence rates of space and time can be obtained at the same time. At last, some numerical examples are given to validate our theorem.

scholarly journals Numerical Solution for Third-Order Two-Point Boundary Value Problems with the Barycentric Rational Interpolation Collocation Method

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Qian Ge ◽  
Xiaoping Zhang
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Rational Interpolation ◽  
Point Boundary ◽  
Third Order ◽  
The Third ◽  
The Matrix ◽  
Barycentric Rational Interpolation

The numerical solution for a kind of third-order boundary value problems is discussed. With the barycentric rational interpolation collocation method, the matrix form of the third-order two-point boundary value problem is obtained, and the convergence and error analysis are obtained. In addition, some numerical examples are reported to confirm the theoretical analysis.

Barycentric Rational Interpolation Iteration Collocation Method for Solving Nonlinear Vibration Problems

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Jian Jiang ◽  
Zhao-Qing Wang ◽  
Jian-Hua Wang ◽  
Bing-Tao Tang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Vibration ◽  
Collocation Method ◽  
Nonlinear Differential Equations ◽  
Rational Interpolation ◽  
Algebraic Equations ◽  
Vibration Problems ◽  
Differential Matrix ◽  
Barycentric Rational Interpolation

In this article, a powerful computational methodology, named as barycentric rational interpolation iteration collocation method (BRICM), for obtaining the numerical solutions of nonlinear vibration problems is presented. The nonlinear vibration problems are governed by initial-value problems of nonlinear differential equations. Given an initial guess value of the unknown function, the nonlinear differential equations can be transformed into linear differential equations. By applying barycentric rational interpolation and differential matrix, the linearized differential equation is discretized into algebraic equations in the matrix form. The latest solution of nonlinear differential equation is obtained by solving the algebraic equations. The numerical solution of nonlinear vibration problem can be calculated by iteration method under given control precision. Then, the velocity and acceleration can be obtained by differential matrix of barycentric rational interpolation, and the period of nonlinear vibration is also computed by BRICM. Some examples of nonlinear vibration demonstrate the proposed methodological advantages of effectiveness, simple formulations, and high precision.

Solution of plane elasticity problems with Mathematica

1995 ◽  
Vol 55 (2) ◽  
pp. 229-236 ◽  
Author(s):  
N.I. Ioakimidis ◽  
G.T. Anastasselos
Keyword(s):  
Plane Elasticity ◽  
Elasticity Problems
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