A Differential Quadrature Algorithm for the Numerical Solution of the Second-Order One Dimensional Hyperbolic Telegraph Equation

In this article, we proposed a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of one dimensional hyperbolic telegraph equation. The hyperbolic partial differential equations model the vibrations of structures (e.g., buildings, beams, and machines) and they are the basis for fundamental equations of atomic physics. The PDQM reduced the problem into a system of second order linear differential equation. Then, the obtained system is changed into coupled differential equations and lastly, RK4 method is used to solve the coupled system. The accuracy of the proposed method is demonstrated by three test examples. The numerical results are found to be in good agreement with the exact solutions. The whole computation work is done with help of software DEV C++ and MATLAB.