Integral equations with diagonal and boundary singularities of the kernel

DOI10.4171/ZAA/1304zbMath1118.45003MaRDI QIDQ873756

Arvet Pedas, Gennadi Vainikko

Publication date: 20 March 2007

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

zbMATH Keywords

boundary singularitiesweighted spacesweakly singular kernelsmoothness of solutionsFredholm integral equation, Volterra integral equation

Mathematics Subject Classification ID

Asymptotics of solutions to integral equations (45M05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (26)

Numerical solution of Volterra integral equations with singularities ⋮ On Volterra integral operators with highly oscillatory kernels ⋮ A projection method for Volterra integral equations in weighted spaces of continuous functions ⋮ Fast and accurate solvers for weakly singular Volterra integral equations in weighted spaces ⋮ A priori mesh grading in collocation solution of noncompact Volterra integral equations with diagonal singularity ⋮ A finite-difference scheme on a graded mesh for solving Cauchy problems with a fractional Caputo derivative in a Banach space ⋮ Superconvergent Nyström and degenerate kernel methods for integral equations of the second kind ⋮ On a class of noncompact weakly singular Volterra integral equations: theory and application to fractional differential equations with variable coefficient ⋮ Numerical methods for Fredholm integral equations with singular right-hand sides ⋮ Asymptotic separation for stochastic Volterra integral equations with doubly singular kernels ⋮ What is the complexity of periodic weakly singular integral equations? ⋮ Smoothing transformation for numerical solution of nonlinear weakly singular Volterra integral equations using quasilinearization and product integration methods ⋮ Spline Collocation for Cordial Volterra Integral Equations ⋮ Superconvergent Nyström and degenerate kernel methods for eigenvalue problems ⋮ Nyström type methods for Fredholm integral equations with weak singularities ⋮ A Collocation Method Based on the Central Part Interpolation for Integral Equations ⋮ A Nyström method for Fredholm integral equations with right-hand sides having isolated singularities ⋮ FAST SOLVERS OF WEAKLY SINGULAR INTEGRAL EQUATIONS OF THE SECOND KIND ⋮ Nyström-quasilinearization method and smoothing transformation for the numerical solution of nonlinear weakly singular Fredholm integral equations ⋮ Spline Collocation-Interpolation Method for Linear and Nonlinear Cordial Volterra Integral Equations ⋮ A Quasi-Fast Solver for Weakly Singular Integral Equations of the Second Kind ⋮ On the regularity of solutions to integral equations with nonsmooth kernels on a union of open intervals ⋮ High-Order Methods for Volterra Integral Equations with General Weak Singularities ⋮ Quadratic Spline Collocation for the Smoothed Weakly Singular Fredholm Integral Equations ⋮ Weakly singular linear Volterra integral equations: a Nyström method in weighted spaces of continuous functions ⋮ Stochastic Volterra integral equations with doubly singular kernels and their numerical solutions

Cites Work

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• The smoothness of the solution to a two-dimensional integral equation with logarithmic kernel
• Regularity of the solution of Hammerstein equations with weakly singular kernel
• Singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel
• The smoothness of solutions to nonlinear weakly singular integral equations
• Singularity preserving Galerkin methods for weakly singular Fredholm integral equations
• Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels
• The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
• The Numerical Solution of Integral Equations of the Second Kind
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Smoothness of Solutions of Volterra Integral Equations with Weakly Singular Kernels

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