Abstract
In this paper, we present a new reproducing kernel-based collocation (RKBC) approach with optimal convergence rate for some classes of boundary value problems (BVPs). The reproducing kernel function (RKF) of the reproducing kernel space (RKS) W2m is a piecewise polynomial of degree 2m−1. We observe that the global convergence orders under L∞, L2, H1 and H2-norms of our method in W2m(m=2,3,4) is 2m, 2m, 2m−1, and 2m−2, which are more efficient than existing reproducing kernel methods (RKMs). Besides, our method can also be easily extended to solve interface problems without losing accuracy. Numerical experiments with detailed discussions on the figures and tables confirm the stability and convergence associated with our proposed numerical approach.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.