Numerical Solution for the Fractional Wave Equation Using Pseudo-Spectral Method Based on the Generalized Laguerre Polynomials

• 作者: Mohamed Adel Mohamed M. Khader Nasser H. Sweilam
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: FRACTIONAL Wave Equation Caputo DERIVATIVE Finite Difference Method LAGUERRE POLYNOMIALS Convergence Analysis
• 年，卷（期）: 2015,（4）
• 页码范围: 647-654
• 页数: 8页
• 分类号: O1

摘要

In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. The properties of Laguerre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which is solved by the finite difference method. An approximate formula of the fractional derivative is given. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. Numerical solutions of FWE are given and the results are compared with the exact solution.