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Finite Difference/Galerkin Finite Element Simulation of the Semi-Linear Wave Equation with Scale-Invariant Damping and Mass and Power Non-Linearity

This study is concern with the numerical solution of the initial boundary value problem (IBVP) for the semilinear scale-invariant wave equation with damping and mass and power non-linearity. Numerical results of the aforementioned IBVP is obtained by using standart Galerkin finite element method (GFEM) for the spatial variable and the temporal variable is discretized with the finite difference method (FDM). The FDM is also used for the discretization of the spatial variable for the accuracy of the numerical results. The obtained numerical results with different numerical schemes are observed compatible. Numerical simulation of the considered problem is given for the different initial conditions.