HIGH ORDER NUMERICAL QUADRATURES TO ONE DIMENSIONAL DELTA FUNCTION INTEGRALS.

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. [ABSTRACT FROM AUTHOR]