Solving wave dispersion equation for dissipative media using homotopy perturbation technique

This investigation develops a third-order explicit approximation to finding the roots of the dispersion relation for water waves that propagate over dissipative media, using homotopy perturbation. The proposed third-order approximation can give an explicit and accurate calculation on the inaccessible roots of the dispersion relation. The homotopy method yields global convergence to the roots. Interestingly, the contours of the domains of attraction of the roots resemble a fractal pattern.