Solving second-order telegraph equations with high-frequency extrinsic oscillations (Q6086854)

The authors consider a second order linear partial differential equation, referred to as the second order telegraph equation with constant coefficients, in unbounded domain. It is shown that the exact solution can be written as the sum of two terms. The first and second terms represent respectively the non-oscillatory and oscillatory parts of the solution. Each of these two terms is written as a series in inverse powers of an oscillatory parameter denoted by \(\omega\). Each coefficient of the non-oscillatory part is the solution of a telegraph equation, without a second member, that can be solved using some suitable methods for this type of equations. The coefficients of the oscillatory part are computed recursively. This approach leads to a method which exhibits improved performance with growing frequency of oscillation.