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Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations
Jihong Wang, Jerry Zhijian Yang, Jiwei Zhang
The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered.…
A unconditionally energy dissipative, adaptive IMEX BDF2 scheme and its error estimates for Cahn-Hilliard equation on generalized SAV approach
Yifan Wei, Jiwei Zhang, Chengchao Zhao +1
An adaptive implicit-explicit (IMEX) BDF2 scheme is investigated on generalized SAV approach for the Cahn-Hilliard equation by combining with Fourier spectral method in space. It i…
On perfectly matched layers of nonlocal wave equations in unbounded multi-scale media
Yu Du, Jiwei Zhang
A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML pr…
Sharp error estimate of variable time-step IMEX BDF2 scheme for parabolic integro-differential equations with initial singularity arising in finance
Chengchao Zhao, Ruoyu Yang, Yana Di +1
The recently developed technique of DOC kernels has been a great success in the stability and convergence analysis for BDF2 scheme with variable time steps. However, such an analys…
Unconditionally optimal error estimate of a linearized variable-time-step BDF2 scheme for nonlinear parabolic equations
Chengchao Zhao, Nan Liu, Yuheng Ma +1
In this paper we consider a linearized variable-time-step two-step backward differentiation formula (BDF2) scheme for solving nonlinear parabolic equations. The scheme is construct…