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

Abstract

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∞ 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.

Keywords

• 35Exx
• 35Qxx
• 65Mxx
• 65Nxx