An equivalent study regarding polynomial DQM and B-spline based DQM via 1D and 2D Hyperbolic Telegraph equation

A discussion of numerical results for $1D$ and $2D$ Hyperbolic Telegraph equations is primary objective of this paper. In this article, Hyperbolic Telegraph equation is addressed using Lagrange Interpolation Polynomial DQM and NUAH B-spline DQM, respectively, as Method I and Method II. In Method I, necessary weighting coefficients are identified using DQM and the Lagrange interpolation polynomial basis function. NUAH B-spline is used in DQM in Method II. Exact and numerical results are represented graphically, and they match across several grid places, confirming effectiveness and simplicity of current approach. $L_{\infty }$ and Absolute errors are shown. It has been observed that results from DQM based on polynomials are superior than those from B-spline based methods. Via error reduction, Method I is more effective. A thorough analysis comparing the errors with the piece of present research is also included to support the argument that polynomial-based DQM is more efficient than B-spline-based DQM.