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April 25, 2026Open Access

Numerical study for 1D and 2D hyperbolic diffusion equation with cubic and quartic hyperbolic B-spline DQM with correlation aspect

Key Points

This study aims to compare cubic and quartic Hyperbolic B-Spline differential quadrature methods for hyperbolic diffusion equations.
Applied cubic and quartic Hyperbolic B-Spline differential quadrature methods to 1D and 2D hyperbolic diffusion equations.
Conducted graphical error trend analysis and stability tests using matrix stability analysis.
Used 't' test to assess the significance of results between the two numerical techniques.
Cubic Hyperbolic B-Spline DQM yielded lower error rates compared to quartic DQM.
Error analysis revealed significant improvements in numerical profiles with cubic B-splines.
Stability analysis confirmed robustness of the cubic method over the quartic.

Abstract

The present study provides a comparison between two numerical techniques: the cubic Hyperbolic B-Spline differential quadrature method and the quartic Hyperbolic B-Spline differential quadrature method. These methods were implemented to discuss numerical simulations of one and two-dimensional Hyperbolic Diffusion Equations. The graphical compatibility of the proposed method was tested by matching the exact and numerical profiles. The validation and robustness of the proposed methods are claimed based on the error analysis. A detailed graphical error trend analysis was performed to understand the tabular results. Furthermore, the correlation aspects of the parameters are discussed in this research. The significance of the results between the two numerical techniques is tested via the ‘t’ test. The stability of the proposed methods is claimed to be as per the matrix stability analysis method. It was observed that the cubic Hyperbolic B-Spline DQM produced better and reduced errors than the quartic Hyperbolic B-Spline DQM.

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