Using matrix stability for variable telegraph partial differential equation

Abstract

The variable telegraph partial differential equation depend on initial boundaryvalue problem has been studied. The coefficient constant time-space telegraphpartial differential equation is obtained from the variable telegraph partialdifferential equation throughout using Cauchy-Euler formula. The first andsecond order difference schemes were constructed for both of coefficient constant time-space and variable time-space telegraph partial differential equation.Matrix stability method is used to prove stability of difference schemes for thevariable and coefficient telegraph partial differential equation. The variabletelegraph partial differential equation and the constant coefficient time-spacetelegraph partial differential equation are compared with the exact solution.Finally, approximation solution has been found for both equations. The erroranalysis table presents the obtained numerical results.