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- W2922898532 startingPage "108886" @default.
- W2922898532 abstract "Different efficient and accurate numerical methods have recently been proposed and analyzed for the nonlinear Klein-Gordon equation (NKGE) with a dimensionless parameter $varepsilonin (0,1]$, which is inversely proportional to the speed of light. In the nonrelativestic limit regime, i.e. $0<varepsilonll1$, the solution of the NKGE propagates waves with wavelength at $O(1)$ and $O(varepsilon^2)$ in space and time, respectively, which brings significantly numerical burdens in designing numerical methods. We compare systematically spatial/temporal efficiency and accuracy as well as $varepsilon$-resolution (or $varepsilon$-scalability) of different numerical methods including finite difference time domain methods, time-splitting method, exponential wave integrator, limit integrator, multiscale time integrator, two-scale formulation method and iterative exponential integrator. Finally, we adopt the multiscale time integrator to study the convergence rates from the NKGE to its limiting models when $varepsilonto0^+$." @default.
- W2922898532 created "2019-04-01" @default.
- W2922898532 creator A5009090425 @default.
- W2922898532 creator A5064750893 @default.
- W2922898532 date "2019-12-01" @default.
- W2922898532 modified "2023-10-10" @default.
- W2922898532 title "Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime" @default.
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- W2922898532 doi "https://doi.org/10.1016/j.jcp.2019.108886" @default.
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