Uniformly accurate exponential-type integrators for klein-gordon equations with asymptotic convergence to classical splitting schemes in the nonlinear schroedinger limit
For computational scientists solving Klein-Gordon equations, this provides robust numerical methods that avoid step-size restrictions and asymptotic expansions, enabling efficient simulation across parameter regimes.
The paper introduces exponential-type integrators for Klein-Gordon equations that are uniformly accurate across relativistic and highly-oscillatory non-relativistic regimes without step-size restrictions, requiring only the same regularity as the limit system. The first- and second-order schemes converge to classical Lie and Strang splittings in the nonlinear Schrödinger limit.
We introduce efficient and robust exponential-type integrators for Klein-Gordon equations which resolve the solution in the relativistic regime as well as in the highly-oscillatory non-relativistic regime without any step-size restriction, and under the same regularity assumptions on the initial data required for the integration of the corresponding limit system. In contrast to previous works we do not employ any asymptotic/multiscale expansion of the solution. This allows us derive uniform convergent schemes under far weaker regularity assumptions on the exact solution. In particular, the newly derived exponential-type integrators of first-, respectively, second-order converge in the non-relativistic limit to the classical Lie, respectively, Strang splitting in the nonlinear Schr{ö}dinger limit.