Compact implicit difference approximation for time-fractional diffusion-wave equation

• Published in: Alexandria engineering journal Vol. 61; no. 5; pp. 4119 - 4126
• Main Authors: Ali, Umair, Iqbal, Azhar, Sohail, Muhammad, Abdullah, Farah Aini, Khan, Zohaib
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2022; Elsevier
• Subjects: Compact approximation; Consistency; Convergence; Fractional diffusion-wave equation; Grünwald Letnikov formula; Implicit difference scheme; Stability; Implicit difference scheme; Stability; Consistency; Compact approximation; Fractional diffusion-wave equation; Grünwald Letnikov formula; Convergence
• ISSN: 1110-0168
• DOI: 10.1016/j.aej.2021.09.005

In this article, developed the compact implicit difference method based Grünwald Letnikov formula (GLF) to compute the solution of the time-fractional diffusion-wave equation (TFDWE) describing wave propagation phenomenan having order α(1<α<2). The fractional derivative is in Caputo sense. The theoretical analysis such as stability, consistency, convergence and solvability of the said scheme are discussed and proved that the scheme is conditionally stable and convergent with the order (τ2+(Δx)4). The numerical results compared with the recent existed method. The results of the numerical examples show that the GLF and the proposed method is very accurate and efficient for time fractional diffusion-wave equation.