The Finite Difference Methods for φ4 Klein-Gordon Equation

We solved4 Klein-Gordon equation numerically by using two finite difference methods: The first is the explicit method and the second is the implicit (Crank-Nicholson) method. Also, we studied the numerical stability of the two methods using Fourier (Von Neumann) method and it has been found that the first method is simpler and has faster convergence while the second method is more accurate, and the explicit method is conditionally stable while the implicit method is unconditionally stable.