Spectral collocation method based on fractional order Legendre polynomials for non-linear fractional integro-differential equations
Yong-Suk Kang, Jin-Ok Jang, Chol-Sim Kim
Faculty of Mathematics, Kim Il Sung University, Pyongyang, Democratic People’s Republic of Korea
Keywords: spectral collocation method, fractional order legendre polynomial, fractional integro-differential equations
Abstract
In this paper, we study a numerical method to approximate a solution with weak singularity at the initial time of non-linear fractional integro-differential equations. For this we use fractional order Legendre polynomials as a basis and reduce the given problem to a finite dimensional problem using a spectral collocation method. We theoretically prove the exponential convergence rate of a function approximation based on the fractional order Legendre polynomials and, on this basis, present an error analysis of the proposed method. We provide some numerical examples to show the convergence rate and efficiency of the proposed method.
|
