A numerical solution of the Klein–Gordon equation and convergence of the decomposition method

摘要

The decomposition method for solving the Klein–Gordon equation has been implemented. The explicit and numerical solutions of the equation are calculated in the form of convergent power series with easily computable components. The present method performs extremely well in terms of accuracy, efficiency, simplicity, stability and reliability. We also proved the convergence of Adomian's decomposition method for the nonlinear Klein–Gordon equation.