Unconditionally stable compact theta schemes for solving the linear and semi-linear fourth-order diffusion equations

作者：

Highlights：

• The compact theta scheme for the linear fourth-order diffusion equations is presented.

• The scheme is unconditionally stable and convergent for any θ ∈ [1/2, 1].

• The compact theta scheme is generalized to the semi-linear problem.

• The effectiveness and accuracy of both schemes are verified by numerical experiments.

摘要

•The compact theta scheme for the linear fourth-order diffusion equations is presented.•The scheme is unconditionally stable and convergent for any θ ∈ [1/2, 1].•The compact theta scheme is generalized to the semi-linear problem.•The effectiveness and accuracy of both schemes are verified by numerical experiments.

论文关键词：Fourth-order diffusion equation,Compact theta scheme,Unconditionally stable,Consistency and convergence,Semi-linear problem

论文评审过程：Received 3 February 2018, Revised 1 September 2018, Accepted 10 September 2018, Available online 1 October 2018, Version of Record 1 October 2018.

论文官网地址：https://doi.org/10.1016/j.amc.2018.09.026