Research PaperNo Access

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

Department of Humanities & Sciences, College of Aeronautical Engineering, National University of Science and Technology, Islamabad, Pakistan

E-mail Address: manzoor366@gmail.com

Corresponding author.

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and

Sirajul Haq

Faculty of Engineering Sciences, GIK Institute of Engineering Sciences and Technology, Topi-23640, Pakistan

E-mail Address: siraj_jcs@yahoo.co.in

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https://doi.org/10.1142/S0129183121500108Cited by:1 (Source: Crossref)

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 $𝒪 (τ^{3 - α}) (1 < α \leq 2)$ 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 $E_{2}$ , $E_{\infty}$ and $E_{rms}$ error norms as well as number of nodes $N$ and time step-size $τ$ .

Keywords:

PACS: 02.30.Jr, 02.60.Cb, 02.60.-x

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