Error estimates for a class of energy dissipative IMEX Runge–Kutta schemes applied to the no-slope-selection thin film model

In this work, we rigorously establish the convergence analysis and error estimates for a class of up to third-order implicit-explicit Runge–Kutta (IMEX RK) schemes for the no-slope-selection (NSS) thin film growth model, which follows from detailed eigenvalue bound estimates for constructed operators and nonlinear analysis of the NSS equation. To our knowledge, this convergence analysis is the first such result of applying a third-order accurate IMEX RK scheme to the epitaxial growth model. Additionally, by introducing a linear stabilization term to the system and employing the Fourier pseudo-spectral method for spatial discretization, we reestablish the energy stability of the first- to third-order IMEX RK schemes in a concise way. Numerical experiments are performed to verify the accuracy of the scheme, and to illustrate some theoretical results such as mass conservation, energy decay rate, and growth rates of surface roughness and mound width.