OICC Press Mathematical Sciences 2251-7456 17 4 (December 2023) 2022 03 06 Advanced shifted sixth-kind Chebyshev tau approach for solving linear one-dimensional hyperbolic telegraph type problem 10.1007/s40096-022-00460-6 EN A. G. Atta Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EG W. M. Abd-Elhameed Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, EG G. M. Moatimid Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, EG Y. H. Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, EG Journal Article 2022 03 06 Abstract A new numerical scheme based on the tau spectral method for solving the linear hyperbolic telegraph type equation is presented and implemented. The derivation of this scheme is based on utilizing certain modified shifted Chebyshev polynomials of the sixth-kind as basis functions. For this purpose, some new formulas concerned with the modified shifted Chebyshev polynomials of the sixth-kind have been stated and proved, and after that, they serve to study the hyperbolic telegraph type equation with our proposed scheme. One advantage of using this scheme is that it reduces the problem into a system of algebraic equations that can be simplified using the Kronecker algebra analysis. The convergence and error estimate of the proposed technique are analyzed in detail. In the end, some numerical tests are presented to demonstrate the efficiency and high accuracy of the proposed scheme.