SINOPSIS

The performance of three solution techniques (finite difference, method of lines, and the generalized integral transform technique) applied to the same one-dimensional hyperbolic wave equation with a temporally oscillating velocity is described. Performance of the algorithms is measured in terms of computational speed to attain the same root-mean-square error (E_rms) compared with the closed-form solution, over the spatial domain at a specified time. While all three techniques were able to attain the strict E_rms, computational times were typically less for the method of lines technique for most alternative conditions simulated. This conclusion is specific to the problem examined and may change for other problems.
Solutions were programmed in MATLAB. Most of the integrals that appeared in the generalized integral transform technique solution were evaluated symbolically by MATLAB to increase accuracy and computational speed.