Proves optimal order-1 and order-2 convergence for an exponential integrator on NLS and corrected Lie splitting on NLW by applying Strichartz and null-form estimates in continuous time.
Error analysis of trigonometric integrators for semilinear Klein-Gordon equations
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Strang splitting for the 3D semilinear wave equation achieves almost order 2 in L2 and order 1 in H1 for cubic nonlinearity under finite energy, with order reduced by 1/2 for quartic, via continuous and discrete Strichartz estimates.
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Improved error estimates for low-regularity integrators using space-time bounds
Proves optimal order-1 and order-2 convergence for an exponential integrator on NLS and corrected Lie splitting on NLW by applying Strichartz and null-form estimates in continuous time.
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Error analysis of the Strang splitting for the 3D semilinear wave equation with finite-energy data
Strang splitting for the 3D semilinear wave equation achieves almost order 2 in L2 and order 1 in H1 for cubic nonlinearity under finite energy, with order reduced by 1/2 for quartic, via continuous and discrete Strichartz estimates.