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Boundary corrections for kernel approximation to differential operators
Andrew Christlieb, Sining Gong, Hyoseon Yang
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional…
Superconvergent Non-Polynomial Approximations
Andrew Christlieb, William Sands, Hyoseon Yang
In this paper, we introduce a superconvergent approximation method that employs radial basis functions (RBFs) in the numerical solution of conservation laws. The use of RBFs for in…
Improving accuracy of the fifth-order WENO scheme by using the exponential approximation space
Youngsoo Ha, Chang Ho Kim, Hyoseon Yang +1
The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential po…
A Kernel-Based Explicit Unconditionally Stable Scheme for Hamilton-Jacobi Equations on Nonuniform Meshes
Andrew Christlieb, William Sands, Hyoseon Yang
In \cite{christlieb2019kernel}, the authors developed a class of high-order numerical schemes for the Hamilton-Jacobi (H-J) equations, which are unconditionally stable, yet take th…