Error estimate of exponential time differencing Runge-Kutta scheme for the epitaxial growth model without slope selection. (English) Zbl 07589950
Summary: In this work, we consider the second order exponential time differencing Runge-Kutta (ETDRK) scheme for solving the epitaxial growth model without slope selection. Based on a linear convex splitting of the energy, by using the Fourier collocation approximation for spatial discretization and applying the ETDRK scheme to the split form of the equation, we propose a second order ETDRK (ETDRK2) scheme for the no-slope-selection epitaxial growth model. We prove the preservation of mass conservation of the ETDRK2 scheme and rigorously establish its error estimate. Several numerical experiments are carried out to verify the accuracy of the scheme. We also simulate the coarsening dynamics with small diffusion coefficients to show the theoretical energy decay rate and the growth rates of the surface roughness and the mound width.
MSC:
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
exponential time differencing Runge-Kutta; thin film growth; linear convex splitting; Fourier collocation; error estimateReferences:
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