Solving nonlinear Telegrapher's equation (non-constant speed)

[Skema_Fish]

Hi
I had a problem with a nonlinear PDE. The equation is 4-D telegraph equation in which the velocity of propagation of the wave is varied with time. If the equation is solved by using the method of separation of variables, then the solution obtained is the Bessel function. The problem is when a parameter (for example, say "a") limit is taken close to zero, then the solution of the telegraph equation approaches zero. In fact, from the telegraph equation itself can be seen that if the parameter limit is taken close to zero then the solution & telegraph equation itself reduces to ordinary wave equation.

The equation is

$\ddot{\psi}$$+{5a}$$\dot{\psi}$ $={\frac{e^{-2at}}{A^{2}}\nabla^{2}\psi}$

the question is: is there something wrong with my calculation method? I followed every step properly but the results are not satisfactory.

 

[gtoguy97]

The answer to your question is that there is likely something wrong with your calculation method. You need to be careful when taking a parameter limit close to zero, as this can lead to numerical issues due to the small number of digits being used in the calculations. Additionally, you should make sure that the equation is properly transformed into the form needed for the separation of variables technique to be applied.