Geology

Collocation method

Volterra integral equation

Bandwidth (computing)

Computer network

Mathematics

Economic growth

Collocation (remote sensing)

Orthogonal collocation

Piecewise

Mathematical analysis

Uniform convergence

Economics

Integral equation

Convergence (economics)

Computer science

Differential equation

Applied mathematics

Singular integral

Ordinary differential equation

Remote sensing

Polynomial

SIAM Journal on Numerical Analysis

Collocation solutions by globally continuous piecewise polynomials to second-kind Volterra integral equations (VIEs) with smooth kernels are uniformly convergent only for certain sets of collocation points. In this paper we establish the analogous convergence theory for VIEs with weakly singular kernels, for both uniform and graded meshes.

The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations