TITLE:
Comparison of Numerical Approximations of One-Dimensional Space Fractional Diffusion Equation Using Different Types of Collocation Points in Spectral Method Based on Lagrange’s Basis Polynomials
AUTHORS:
Mushfika Hossain Nova, Hasib Uddin Molla, Sajeda Banu
KEYWORDS:
Fractional Diffusion Equation, Spectral Method, Collocation Method, Lagrange’s Basis Polynomial
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.4,
December
15,
2017
ABSTRACT: Recently many research works
have been conducted and published regarding fractional order differential
equations. There are several approaches available for numerical approximations
of the solution of fractional order diffusion equations. Spectral collocation
method based on Lagrange’s basis polynomials to approximate numerical solutions
of one-dimensional (1D) space fractional diffusion equations are introduced in
this research paper. The proposed form of approximate solution satisfies
non-zero Dirichlet’s boundary conditions on both boundaries. Collocation scheme
produce a system of first order Ordinary Differential Equations (ODE) from the
fractional diffusion equation. We applied this method with four different sets
of collocation points to compare their performance.