The fine error estimation of collocation methods on uniform meshes for weakly singular Volterra integral equations

DOI10.1007/s10915-020-01266-1zbMath1456.65184OpenAlexW3038252137MaRDI QIDQ777033

Hui Liang, Hermann Brunner

Publication date: 13 July 2020

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-020-01266-1

zbMATH Keywords

convergence analysiscollocation methodsVolterra integral equationsweakly singular kernelsuniform meshes

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Volterra integral equations (45D05) Singular integral equations (45E99)

Related Items

Polynomial spline collocation method for solving weakly regular Volterra integral equations of the first kind, Discontinuous Galerkin approximations to second-kind Volterra integral equations with weakly singular kernel, A combination method for solving multi-dimensional systems of Volterra integral equations with weakly singular kernels, Finite element approximation for Maxwell's equations with Debye memory under a nonlinear boundary feedback with delay, A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel, Comparison between Taylor and perturbed method for Volterra integral equation of the first kind

Cites Work

• Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices
• Weakly Singular Discrete Gronwall Inequalities
• A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• The Convergence of Collocation Solutions in Continuous Piecewise Polynomial Spaces for Weakly Singular Volterra Integral Equations