Numerical methods for a Volterra integral equation with nonsmooth solutions

DOI10.1016/j.cam.2005.10.019zbMath1092.65119OpenAlexW2143933531MaRDI QIDQ818196

Neville J. Ford, Teresa Diogo, Svilen S. Valtchev, Pedro M. Lima

Publication date: 24 March 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2005.10.019

zbMATH Keywords

convergencenumerical exampleserror boundmultiple solutionssingular kernelEuler's methodproduct integration methodstrapezoidal methodSingular Volterra integral equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Volterra integral equations (45D05)

Related Items (13)

Two reliable methods for solving the Volterra integral equation with a weakly singular kernel ⋮ Approximate solution of the system of linear Volterra-Stieltjes integral equations of the second kind ⋮ Solution of nonlinear weakly singular Volterra integral equations using the fractional-order Legendre functions and pseudospectral method ⋮ Convergence analysis of spectral collocation methods for a class of weakly singular Volterra integral equations ⋮ Analytic and numerical analysis of some statistical features of fragmentation processes ⋮ Modified Euler's method with a graded mesh for a class of Volterra integral equations with weakly singular kernel ⋮ Solution of a class of Volterra integral equations with singular and weakly singular kernels ⋮ A Sparse Spectral Method for Volterra Integral Equations Using Orthogonal Polynomials on the Triangle ⋮ Approximate solution of Volterra-Stieltjes linear integral equations of the second kind with the generalized trapezoid rule ⋮ A Nyström interpolant for some weakly singular linear Volterra integral equations ⋮ On a graded mesh method for a class of weakly singular Volterra integral equations ⋮ Adaptive collocation methods for Volterra integral and integro-differential equations ⋮ Numerical analysis of a singular integral equation

Cites Work

• Unnamed Item
• Numerical modelling of qualitative behaviour of solutions to convolution integral equations
• Product integration methods for an integral equation with logarithmic singular kernel
• Existence, uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels
• An extrapolation method for a Volterra integral equation with weakly singular kernel
• Numerical solution of a nonuniquely solvable Volterra integral equation using extrapolation methods
• High order product integration methods for a Volterra integral equation with logarithmic singular kernel
• Numerical analysis of a singular integral equation

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