Numerical simulation of higher-order diffusion-wave equations of variable coefficients using the meshless spectral method

Manzoor Hussain and Sirajul Haq ()
Additional contact information
Manzoor Hussain: Department of Humanities & Sciences, College of Aeronautical Engineering, National University of Science and Technology, Islamabad, Pakistan
Sirajul Haq: #x2020;Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi-23640, Pakistan

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 01, 1-19

Abstract: In this paper, meshless spectral interpolation technique using implicit time stepping scheme is proposed for the numerical simulations of time-fractional higher-order diffusion wave equations (TFHODWEs) of variable coefficients. Meshless shape functions, obtained from radial basis functions (RBFs) and point interpolation method (PIM), are used for spatial approximation. Central differences coupled with quadrature rule of 𝒪(τ3−α) (1<α≤2) are employed for fractional temporal approximation. For advancement of solution, an implicit time stepping scheme is then invoked. Simulations performed for different benchmark test problems feature good agreement with exact solutions. Stability analysis of the proposed method is theoretically discussed and computationally validated to support the analysis. Accuracy and efficiency of the proposed method are assessed via E2, E∞ and Erms error norms as well as number of nodes N and time step-size τ.

Keywords: Meshless spectral interpolation method; radial point interpolation method; diffusion-wave equation; Caputo fractional derivative; stability analysis (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0129183121500108
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijmpcx:v:32:y:2021:i:01:n:s0129183121500108

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0129183121500108

Access Statistics for this article

International Journal of Modern Physics C (IJMPC) is currently edited by H. J. Herrmann

More articles in International Journal of Modern Physics C (IJMPC) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().