Differential Quadrature Solution of Hyperbolic Telegraph Equation

<table>Numerical and exact solutions at different times for Problem 1, with <svg height="11.1" id="M185" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 63.037498 11.1" width="63.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">Δ</tspan>
<tspan style="font-size: 12.50px; " x="9.0271664" y="0">𝑡</tspan>
<tspan style="font-size: 12.50px; " x="16.403936" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="28.444324" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="34.695824" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="37.821575" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="44.073074" y="0">5</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.8125" id="M186" style="vertical-align:-0.10033pt" version="1.1" viewbox="0 0 48.4375 10.8125" width="48.4375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.8125)">
<g transform="translate(72,-63.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="14.103384" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="32.395271" y="0">7</tspan>
</text>
</g>
</g>
</svg> using Neumann boundary conditions.</table>

Journal of Applied Mathematics

Differential Quadrature Solution of Hyperbolic Telegraph Equation

Figure 1