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Keywords

Klein-Gordon equation
Finite difference methods
explicit method
implicit (Crank-Nicholson) method
numerical stability
Fourier (Von Neumann) method
Convergence

Abstract

We solved φ4 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.  
https://doi.org/10.33899/csmj.2008.163970
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