## SOLVABILITY THE TELEGRAPH EQUATION WITH PURELY INTEGRAL CONDITIONS

## SOLVABILITY THE TELEGRAPH EQUATION WITH PURELY INTEGRAL CONDITIONS

*A. Merad, A. Bouziani*

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## Abstract

In this paper a numerical technique is developed for the one-dimensional telegraph equation, we prove the existence, uniqueness, and continuous dependence upon the data of solution to a telegraph equation with purely integral conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution by using a simple and efficient algorithm for numerical solution.

## Keywords

Telegraph equation, purely integral conditions, a priori estimates, Laplace transform method.