Uniform l1 behavior of the first-order interpolant quadrature scheme for some partial integro-differential equations. (July 2021)

• Record Type: Journal Article
• Authors: Xu, Da
• Is Part Of: Applied mathematics letters. Volume 117(2021)
• Publication Date: 2021-07
• Subjects: Evolution equation -- Weakly singular kernel -- Non-smooth data -- Interpolating quadrature -- Error estimates; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2021.107097
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We study the time discretization for the solution of a Volterra equation with weakly singular kernel. The time discrete scheme is based on the first-order backward difference method. The memory term is approximated by the interpolating quadrature. We use Laplace transform technique to show that this interpolating quadrature scheme has a convergence rate of O ( △ t ) where △ t denotes the time step, for smooth and non-smooth initial data in homogeneous case. Special attention is that the uniform l 1 convergence property of the discretization in time is given.