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Numerical Quadrature Formulas Associated with the Integration of Rapidly Oscillating Functions

In: Dimensionality Reducing Expansion of Multivariate Integration

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  • Tian-Xiao He

    (Illinois Wesleyan University, Department of Mathematics & Computer Sience)

Abstract

In Sections 1 and 2, we will discuss numerical quadrature for a type of double integrals and for oscillatory integrals, respectively. The compound degree of precision of the approximate computation of oscillatory integrals will be looked at in Section 3. Section 4 will give a fast numerical computation technique shown in Bradie, Coifman, and Grossmann [2] for treating model oscillatory boundary integral operators with or without singularities in ℝ2. Finally, we will apply Burrows’ DRE ([6]) to numerical integration in Section 5. Burrows’ DRE is an exact DRE, which can reduce multidimensional Lebesgue integrals to one-dimensional integrals of measure functions. This technique is particularly useful for integrands that are highly oscillatory in character or are singular. The corresponding error analysis for finding measure functions will be given in Section 6.

Suggested Citation

  • Tian-Xiao He, 2001. "Numerical Quadrature Formulas Associated with the Integration of Rapidly Oscillating Functions," Springer Books, in: Dimensionality Reducing Expansion of Multivariate Integration, chapter 0, pages 109-149, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-2100-5_4
    DOI: 10.1007/978-1-4612-2100-5_4
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