Fast non-polynomial interpolation and integration for functions with logarithmic singularities
Provides faster interpolation and integration methods for functions with logarithmic singularities, which is a specific computational problem in numerical analysis.
The paper proposes a fast non-polynomial interpolation for functions with logarithmic singularities, executed via discrete cosine transform, and a new quadrature for logarithmically singular integrals. Numerical examples validate the efficiency of both methods.
A fast non-polynomial interpolation is proposed in this paper for functions with logarithmic singularities. It can be executed fast with the discrete cosine transform. Based on this interpolation, a new quadrature is proposed for a kind of logarithmically singular integrals. The interpolation and integration errors are also analyzed. Numerical examples of the interpolation and integration are shown to validate the efficiency of the proposed new interpolation and the new quadrature.