Advanced shifted sixth-kind Chebyshev tau approach for solving linear one-dimensional hyperbolic telegraph type problem

Abstract A new numerical scheme based on the tau spectral method for solving linear hyperbolic telegraph type equation is presented and implemented. The derivation of this utilizing certain modified shifted Chebyshev polynomials sixth-kind as basis functions. For purpose, some formulas concerned with have been stated proved, after that, they serve to study our proposed scheme. One advantage using that it reduces problem into a system algebraic equations can be simplified Kronecker algebra analysis. convergence error estimate technique are analyzed in detail. In end, tests demonstrate efficiency high accuracy