scholarly journals Linear Barycentric Rational Method for Two-Point Boundary Value Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Qian Ge ◽  
Xiaoping Zhang
Keyword(s):  
Theoretical Analysis ◽  
Convergence Rate ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Rational Method ◽  
Matrix Form ◽  
Point Boundary ◽  
Numerical Examples ◽  
The Matrix

Linear barycentric rational method for solving two-point boundary value equations is presented. The matrix form of the collocation method is also obtained. With the help of the convergence rate of the interpolation, the convergence rate of linear barycentric rational collocation method for solving two-point boundary value problems is proved. Several numerical examples are provided to validate the theoretical analysis.

A Collocation Method for Global Approximation of General Second Order BVPs

2007 ◽  
Vol 3 (1) ◽  
pp. 23-34 ◽  
Author(s):  
F. Costabile ◽  
A. Napoli
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Collocation Method ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
Global Approximation ◽  
Numerical Examples

For the numerical solution of the second order nonlinear two-point boundary value problems a family of polynomial global methods is derived.Numerical examples provide favorable comparisons with other existing methods.

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.

scholarly journals Spectral approximations to the fractional integral and derivative

2012 ◽  
Vol 15 (3) ◽  
Author(s):  
Changpin Li ◽  
Fanhai Zeng ◽  
Fawang Liu
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Caputo Derivative ◽  
Initial Value Problems ◽  
Fractional Integral ◽  
Jacobi Polynomials ◽  
Boundary Value ◽  
Initial Value ◽  
Numerical Examples ◽  
Spectral Approximations

AbstractIn this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

scholarly journals Alternative methods for solving nonlinear two-point boundary value problems

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 371-374
Author(s):  
Fateme Ghomanjani ◽  
Stanford Shateyi
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Bernstein Polynomials ◽  
Nonlinear Problems ◽  
Alternative Methods ◽  
Point Boundary ◽  
Numerical Examples ◽  
Curve Method ◽  
Linear And Nonlinear

Abstract In this sequel, the numerical solution of nonlinear two-point boundary value problems (NTBVPs) for ordinary differential equations (ODEs) is found by Bezier curve method (BCM) and orthonormal Bernstein polynomials (OBPs). OBPs will be constructed by Gram-Schmidt technique. Stated methods are more easier and applicable for linear and nonlinear problems. Some numerical examples are solved and they are stated the accurate findings.

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