A semi-analytical solution of Hunter–Saxton equation

In this paper, we discretize time derivative terms by a forward difference scheme and linearize thenonlinear terms using a quasilinearization technique to reduce the original equation into a system ofordinary differential equations. Then the Haar wavelet quasilinearization approach is applied to computethe numerical solutions of the Hunter–Saxton equation. Computer simulations show that our obtainedresults are in a good agreement with the exact solution.

Haar wavelets; Hunter-Saxton equation; Adomian decomposition method; Quasilinearization techniqe; Analytical solution