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Numerical accuracy and stability of semilinear Klein--Gordon equation in de Sitter spacetime (2211.09031v1)
Published 16 Nov 2022 in math.NA, cs.NA, and gr-qc
Abstract: Numerical simulations of the semilinear Klein--Gordon equation in the de Sitter spacetime are performed. We use two structure-preserving discrete forms of the Klein--Gordon equation. The disparity between the two forms is the discretization of the differential term. We show that one of the forms has higher numerical stability and second-order numerical accuracy with respect to the grid, and we explain the reason for the instability of the other form.