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.
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