An efficient and fast parallel method for Volterra integral equations of Abel type

DOI10.1016/j.cam.2005.03.056zbMath1101.65117OpenAlexW2090968451MaRDI QIDQ818204

Giovanni Capobianco, Dajana Conte

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.2005.03.056

zbMATH Keywords

Laplace transformconvergencenumerical experimentsparallel computationwaveform relaxation methodsconvolution integralsChebyshev polynomial accelerationfast convolution algorithmTalbot contours

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical methods for integral equations (65R20) Parallel numerical computation (65Y05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

Related Items (10)

Spectral methods for weakly singular Volterra integral equations with pantograph delays ⋮ Non-stationary wave relaxation methods for general linear systems of Volterra equations: convergence and parallel GPU implementation ⋮ Optimal Schwarz waveform relaxation for fractional diffusion-wave equations ⋮ Multistep collocation methods for Volterra integro-differential equations ⋮ Implementation of general linear methods for Volterra integral equations ⋮ Triangular functions for operational matrix of nonlinear fractional Volterra integral equations ⋮ Parallel methods for weakly singular Volterra integral equations on GPUs ⋮ GPU-acceleration of waveform relaxation methods for large differential systems ⋮ High performance parallel numerical methods for Volterra equations with weakly singular kernels ⋮ Spectral methods for weakly singular Volterra integral equations with smooth solutions

Cites Work

• A nonlinear weakly singular Volterra integro-differential equation arising from a reaction-diffusion study in a small cell
• A parallel fast convergent waveform relaxation method for Volterra integral equations.
• The Tchebychev iteration for nonsymmetric linear systems
• Non-reflecting boundary conditions for Maxwell's equations
• Nonstationary waveform relaxation methods for Abel integral equations
• Continuous and discrete time waveform relaxation methods for Volterra integral equations with weakly singular kernels
• Convolution quadrature time discretization of fractional diffusion-wave equations
• The Accurate Numerical Inversion of Laplace Transforms
• A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform
• Fast Convolution for Nonreflecting Boundary Conditions
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