Modified Gauss rules for approximate calculation of some strongly singular integrals

Modified Gauss rules for approximate calculation of some strongly singular integrals

The approach we follow consists in transforming the numerical evaluation of hypersingular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are prese...

Gauss-chebyshev Quadrature Formulae for Strongly Singular Integrals

This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. T...

Calculation of Gauss Quadrature Rules

Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for c...

Symmetric Gauss - Lobattoand Modified Anti - Gauss Rules

Quadrature Rules for Fuzzy Integrals