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

• 作者: Hasib Uddin Molla Mushfika Hossain Nova Sajeda Banu
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Fractional Diffusion Equation Spectral METHOD COLLOCATION METHOD Lagrange’s BASIS POLYNOMIAL
• 年，卷（期）: 2017,（4）
• 页码范围: 469-480
• 页数: 12页
• 分类号: O1

摘要

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.