Spectral Galerkin treatment of linear one-dimensional telegraph type problem via the generalized Lucas polynomials

Abstract The major goal of this research is to develop and test a numerical technique for solving linear one-dimensional telegraph problem. generalized polynomials, namely, the Lucas polynomials are selected as basis functions. To solve type equation, we instead its corresponding integral equation via application spectral Galerkin method that serves convert with underlying conditions into system algebraic equations may be solved by suitable solver. convergence error analysis expansion discussed in depth. current based on assumption problem’s solution separable. Finally, some explanatory examples displayed together comparisons other articles, demonstrate suggested method’s validity, applicability, accuracy.