A new reproducing kernel-based collocation method with optimal convergence rate for some classes of BVPs

作者：

Highlights：

• The proposed methods are of optimal accuracy under the L∞,L2,H1 and H2 norms, that is, of order k+1,k+1,k and k−1, respectively, where k=2m−1 in W2m is the degree of the basis functions.

• The proposed methods are still valid in W22.

• The proposed methods can easily deal with any kind of boundary conditions as well as interface conditions.

摘要

•The proposed methods are of optimal accuracy under the L∞,L2,H1 and H2 norms, that is, of order k+1,k+1,k and k−1, respectively, where k=2m−1 in W2m is the degree of the basis functions.•The proposed methods are still valid in W22.•The proposed methods can easily deal with any kind of boundary conditions as well as interface conditions.

论文关键词：Boundary value problems,Interface problems,Reproducing kernel,Collocation methods,Optimal convergence

论文评审过程：Received 30 November 2020, Revised 18 October 2021, Accepted 17 June 2022, Available online 2 July 2022, Version of Record 2 July 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127343