Author

Li-Lian Wang

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Preprint Sep 2026

A Matrix-free Augmented High Order Compact Solver for Variable-Coefficient Biharmonic Problems

We propose an augmented high-order compact finite difference method for biharmonic equations with clamped boundary conditions and variable coefficients. Standard mixed-type formulations introduce an auxiliary variable, but its boundary values are unavailable, leaving the resulting discrete systems globally coupled and...

Jin Li, Ke-Jia Pan, Xu Qian et al. · 0 citations

Preprint Sep 2026

Well-Conditioned Birkhoff-Collocation Methods for Elliptic-type Problems in Multiple Dimensions

Collocation methods based on Birkhoff interpolation at Gaussian-type points are well-conditioned for one-dimensional initial and boundary value problems [Wang et al., {\em SIAM J. Sci. Comput.} 36 (2014)], but the underlying construction does not extend directly to multiple dimensions. We address the long-standing ill-...

Shun-Chang Li, Zi-Xuan Gao, Yu-Jian Jiao et al. · 0 citations