Pell coefficient polynomials for solving linear hyperbolic first-order partial differential equations via the Tau approach

The main aims of this study are the introduction of Pell coefficient polynomials and their numerical treatment of the first-order hyperbolic partial differential equations. Our suggested numerical algorithm will be derived from the utilization of some novel formulas of the Pell coefficient polynomials, along with the application of the spectral tau method. For the proposed expansion, we investigate the convergence and error estimations in detail. The presented numerical results indicate that the suggested numerical method is accurate, converges exponentially, and is computationally efficient.