Point-wise errors of two conservative difference schemes for the Klein–Gordon–Schrödinger equation

In this study, point-wise errors of two conservative difference schemes for solving the Klein–Gordon–Schrödinger equation are studied. Besides the standard techniques of the energy method, some new techniques are used to prove that the difference solution converges to the exact solution with second order in the discrete L∞L∞ norm. Numerical examples support the theoretical analysis.

► We improved the proof of the convergence of the difference scheme in [30].
► We proved the maximum norm error bound of the difference scheme in [30].
► We construct a new difference scheme and obtained the maximum norm error bound.