We discuss the approximation of integrals of type I(f;t)=∫Rf(x)K(x,t)e-x2|x|αdx,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 K1(x,t)=sin(tx2),K2(x,t)=cos(tx2). Weighted error estimates in uniform and L1 norm are stated and numerical examples to confirm the efficiency of the proposed procedures are given.
The numerical computation of some integrals on the real line
OCCORSIO, Donatella
2000-01-01
Abstract
We discuss the approximation of integrals of type I(f;t)=∫Rf(x)K(x,t)e-x2|x|αdx,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 K1(x,t)=sin(tx2),K2(x,t)=cos(tx2). Weighted error estimates in uniform and L1 norm are stated and numerical examples to confirm the efficiency of the proposed procedures are given.File in questo prodotto:
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