Numerical Analysis of the Telegraph Equation with an Integral Condition

In this paper, an alternative method for accurately and efficiently modeling for the onedimensional Telegraph equation that combines classical and integral boundary conditions is presented. New matrix formulation technique with arbitrary polynomial bases is proposed for the numerical/analytical solution of this kind of partial differential equation. Not only the exact solutions have been achieved by the known forms of the series solutions, but also for the finite terms of series, the corresponding numerical approximations have been computed. I give a simple and efficient algorithm based on an iterative process for numerical solution of the method. Some numerical examples are included to demonstrate the validity and applicability of the technique. 2000 mathematics subject classification: 65M70; 35L15; 35L20; 35P05