Quantitative evaluations of stability and convergence for solutions of semilinear Klein--Gordon equation
arXiv:2508.216591 citationsh-index: 12
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For researchers solving semilinear Klein-Gordon equations numerically, this provides practical evaluation criteria, but the contribution is incremental.
This paper proposes quantitative evaluation methods for stability and convergence of numerical solutions to the semilinear Klein-Gordon equation, and identifies appropriate threshold values by varying initial amplitude and mass.
We perform some simulations of the semilinear Klein--Gordon equation with a power-law nonlinear term and propose each of the quantitative evaluation methods for the stability and convergence of numerical solutions. We also investigate each of the thresholds in the methods by varying the amplitude of the initial value and the mass, and propose appropriate values.