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

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.