High Order Numerical Quadratures to One Dimensional Delta Function Integrals

Authors:
Xin Wen
Affiliations:
wenxin@amss.ac.cn
Venue:
SIAM Journal on Scientific Computing
Year:
2008

Citing 0
Cited 4

High order numerical methods to two dimensional delta function integrals in level set methods

Journal of Computational Physics
A High Order Numerical Method for Computing Physical Observables in the Semiclassical Limit of the One-Dimensional Linear Schrödinger Equation with Discontinuous Potentials

Journal of Scientific Computing
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods

SIAM Journal on Scientific Computing
A Hybrid Phase Flow Method for Solving the Liouville Equation in a Bounded Domain

SIAM Journal on Numerical Analysis

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Abstract

We study high order numerical quadratures to one dimensional delta function integrals in this paper. This is motivated by the fact that traditional numerical quadratures give only first order accuracy in general. We provide criteria on discrete delta functions and support size formulas which ensure any desired accuracy of the numerical quadratures. Discrete delta functions and support size formulas satisfying these criteria are designed. Numerical examples are presented to verify the performed analysis and the high order accuracy of the proposed numerical quadratures.