A Spectral Collocation Method for Nonlinear Fractional Boundary Value Problems with a Caputo Derivative

2017 ◽  
Vol 76 (1) ◽  
pp. 166-188 ◽  
Author(s):  
Chuanli Wang ◽  
Zhongqing Wang ◽  
Lilian Wang
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Caputo Derivative ◽  
Boundary Value ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Fractional Boundary Value Problems

scholarly journals Rational Spectral Collocation Combined with the Singularity Separated Method for a System of Singularly Perturbed Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Lufeng Yang
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Numerical Experiments ◽  
Original Problem ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Barycentric Form ◽  
Theoretical Results

A novel rational spectral collocation method is presented combined with the singularity-separated technique for a system of singularly perturbed boundary value problems. The solution is expressed as u=w+v, where w is the solution of the corresponding auxiliary boundary value problem and v is a singular correction with explicit expressions. The rational spectral collocation method in barycentric form with the sinh transformation is applied to solve the auxiliary third boundary problem. The parameters of the singular correction can be determined by the boundary conditions of the original problem. Numerical experiments are carried out to support theoretical results and provide a favorable comparison with research results of other work.

Eigenvalue comparison for fractional boundary value problems with the Caputo derivative

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Johnny Henderson ◽  
Nickolai Kosmatov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Caputo Derivative ◽  
Boundary Value ◽  
Positive Operators ◽  
Fractional Boundary Value Problem ◽  
Comparison Results ◽  
Eigenvalue Comparison ◽  
Fractional Boundary Value Problems

AbstractWe apply the theory for u 0-positive operators to obtain eigenvalue comparison results for a fractional boundary value problem with the Caputo derivative.

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.

Sign in / Sign up

Export Citation Format

Share Document