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The numerical computation of some integrals on the real line

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
115
Identifiers
DOI: 10.1016/s0377-0427(99)00299-x
Disciplines
  • Mathematics

Abstract

Abstract We discuss the approximation of integrals of type I(f;t)= ∫ R f(x)K(x,t) e −x 2 |x| α dx, α>−1 , K is the weakly singular algebraic kernel |x−t| λ, −1<λ<0, for “large” value of the parameter t. Moreover, we consider strongly oscillatory kernels of type K 1(x,t)= sin(tx 2), K 2(x,t)= cos(tx 2) . Weighted error estimates in uniform and L 1 norm are stated and numerical examples to confirm the efficiency of the proposed procedures are given.

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