A hybrid collocation method for the computational study of multi-term time fractional partial differential equations. (15th December 2022)

• Record Type: Journal Article
• Authors: Ghafoor, Abdul; Khan, Nazish; Hussain, Manzoor; Ullah, Rahman
• Is Part Of: Computers & mathematics with applications. Volume 128(2022)
• Page Start: 130
• Page End: 144
• Publication Date: 2022-12-15
• Subjects: Caputo fractional derivative -- Quadrature formula -- Haar wavelet -- Fractional PDEs -- Quasilinearization; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.10.005
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this article, we focus on the numerical study of one and two dimensional higher order multi-term time fractional partial differential equations. In the adopted strategy, the temporal fractional derivative is replaced via well known L 1 formula and the integer order space derivatives are approximated by truncated one and two dimensional wavelet series. The fascinating nature of the scheme is to use collocation approach which convert the governing equations to the system of algebraic equations from which the wavelet coefficients can be calculated. Next, stability of the proposed scheme is investigated theoretically which is also the fundamental subject of the current work. Further computational convergence rate is computed which predicts that the order is approximately two. The scheme is applied to solve one dimensional beam models (fourth order partial differential equations) and two dimensional fissured rock models (Sobolev equations). Efficiency of the scheme is examined with the help of various error norms such as I ∞, I r m s and I 2 . Simulations indicate pretty much good results from which we can say that the scheme is suitable and robust for both one and two dimensional problems.