Numerical solution of the Harry Dym equation using Chebyshev spectral method via Lie group method

This study represents the solution of the Harry Dym equation (HDE) that was calculated using the Lie symmetry group method. This method transforms the controlled partial differential equation with boundary and initial conditions to the problem that containing boundary value of ordinary differential equation. The Chebyshev spectral approximation method is used to solve this problem numerically. This approach is performing by using the highest order derivatives of Chebyshev approximations, as starting steps, followed by getting approximations to the derivatives of lower order. Our obtained numerical results were compared with other works is done. It is seen that the proposed method for the Harry Dym equation gives more accurate results comparing with mentioned works.