Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm–Liouville problems

2010 ◽  
Vol 217 (5) ◽  
pp. 2266-2276 ◽  
Author(s):  
Xuecang Zhang
Keyword(s):  
Matrix Method ◽  
Differentiation Matrix ◽  
Sturm Liouville ◽  
Chebyshev Differentiation Matrix

Roundoff Error in Computing Derivatives Using the Chebyshev Differentiation Matrix

1995 ◽  
Vol 116 (2) ◽  
pp. 380-383 ◽  
Author(s):  
Alvin Bayliss ◽  
Andreas Class ◽  
Bernard J. Matkowsky
Keyword(s):  
Roundoff Error ◽  
Differentiation Matrix ◽  
Chebyshev Differentiation Matrix

scholarly journals A Reliable Method for Solving Fractional Sturm–Liouville Problems

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 176 ◽  
Author(s):  
M. Khashshan ◽  
Muhammed Syam ◽  
Ahlam Al Mokhmari
Keyword(s):  
Matrix Method ◽  
Reliable Method ◽  
Operational Matrix ◽  
Liouville Problem ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Sturm Liouville

In this paper, a reliable method for solving fractional Sturm–Liouville problem based on the operational matrix method is presented. Some of our numerical examples are presented.

Numerical Solution of Bending Problem for Elliptical Plate Using Differentiation Matrix Method Based on Barycentric Lagrange Interpolation

2014 ◽  
Vol 638-640 ◽  
pp. 1720-1724 ◽  
Author(s):  
Zhao Qing Wang ◽  
Jian Jiang ◽  
Bing Tao Tang ◽  
Wei Zheng
Keyword(s):  
Boundary Conditions ◽  
Governing Equation ◽  
Matrix Method ◽  
Lagrange Interpolation ◽  
Numerical Solutions ◽  
Algebraic Equations ◽  
Uniform Load ◽  
Tensor Form ◽  
Elliptical Plate ◽  
Differentiation Matrix

A differentiation matrix method based on barycentric Lagrange interpolation for numerical analysis of bending problem for elliptical plate is presented. Embedded the elliptical domain into a rectangular, the barycentric Lagrange interpolation in tensor form is used to approximate unknown function. The governing equation of bending plate is discretized by the differentiation matrix derived from barycentric Lagrange interpolation to form a system of algebraic equations. The boundary conditions on curved boundary are directly discretized using barycentric Lagrange interpolation. Combining discrete algebraic equations of governing equation and boundary conditions to form an over-constraints system of equations, the numerical solutions on rectangular can be obtained by solving it. Then, the numerical solutions on elliptical domain are obtained by interpolating the data on rectangular. Numerical results of elliptical plate with uniform load illustrate the effectiveness and accuracy of the proposed method.

Matrix method for solving the Sturm-Liouville problem

1991 ◽  
Vol 54 (2) ◽  
pp. 786-792
Author(s):  
B. Izbasarov ◽  
A. F. Kalaida
Keyword(s):  
Matrix Method ◽  
Liouville Problem ◽  
Sturm Liouville

scholarly journals A matrix method for fractional Sturm-Liouville problems on bounded domain

2017 ◽  
Vol 43 (6) ◽  
pp. 1377-1401 ◽  
Author(s):  
Paolo Ghelardoni ◽  
Cecilia Magherini
Keyword(s):  
Bounded Domain ◽  
Matrix Method ◽  
Sturm Liouville

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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