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- W91441503 abstract "High-fidelity numerical solution of hyperbolic differential equations for functions with jump discontinuities presents a particular challenge. In general, fixed-stencil high-order numerical methods are unstable at discontinuities, resulting in exponential temporal growth of dispersive errors (Gibbs phenomena). Schemes utilizing adaptive stencils have shown to be effective in simultaneously providing high-order accuracy and long-time stability. In this Thesis, the elementary formulation of adaptive-stenciling is described in the finite difference context. Basic formulations are provided for three adaptive-stenciling methods: essentially non-oscillatory (ENO), weighted essentially non-oscillatory (WENO), and energy-stable weighted essentially non-oscillatory (ESWENO) schemes. Examples are presented to display some of the relevant properties of these schemes in solving one-dimensional and two-dimensional linear and nonlinear hyperbolic differential equations with discontinuities." @default.
- W91441503 created "2016-06-24" @default.
- W91441503 creator A5005134123 @default.
- W91441503 date "2010-09-30" @default.
- W91441503 modified "2023-09-23" @default.
- W91441503 title "Comparative Assessment of Adaptive-Stencil Finite Difference Schemes for Hyperbolic Equations with Jump Discontinuities" @default.
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