High performance parallel numerical methods for Volterra equations with weakly singular kernels

DOI10.1016/j.cam.2008.03.027zbMath1169.65118OpenAlexW2073144604MaRDI QIDQ1019660

Ida Del Prete, Giovanni Capobianco, Dajana Conte

Publication date: 4 June 2009

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.2008.03.027

zbMATH Keywords

convergencenumerical experimentsparallel computationwaveform relaxation methodsfractional linear multistep formulaVolterra equations with weakly singular kernels

Mathematics Subject Classification ID

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

Solution of nonlinear weakly singular Volterra integral equations using the fractional-order Legendre functions and pseudospectral method, An analytical and approximate solution for nonlinear Volterra partial integro-differential equations with a weakly singular kernel using the fractional differential transform method, 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, 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, Common solution to a pair of nonlinear Fredholm and Volterra integral equations and nonlinear fractional differential equations, Spectral methods for weakly singular Volterra integral equations with smooth solutions, Nonstationary waveform relaxation methods for Abel integral equations, Modified Chebyshev collocation method for delayed predator-prey system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A nonlinear weakly singular Volterra integro-differential equation arising from a reaction-diffusion study in a small cell
• A family of methods for Abel integral equations of the second kind
• An efficient and fast parallel method for Volterra integral equations of Abel type
• A parallel algorithm for large systems of Volterra integral equations of Abel type
• A parallel fast convergent waveform relaxation method for Volterra integral equations.
• Fast numerical solution of weakly singular Volterra integral equations
• Time point relaxation methods for Volterra integro-differential equations
• Discrete-time waveform relaxation Volterra-Runge-Kutta methods: Convergence analysis
• Convergence of discrete-time relaxation methods based on Volterra backward differentiation formulas
• Wave propagation in media with singular memory
• Convergence results for continuous-time waveform methods for Volterra integral equations
• Continuous and discrete time waveform relaxation methods for Volterra integral equations with weakly singular kernels
• FRACTIONAL DIFFUSIVE WAVES
• Convolution quadrature time discretization of fractional diffusion-wave equations
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
• Error Estimates with Sharp Constants for a Fading Memory Volterra Problem in Linear Solid Viscoelasticity
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Optimal long-time \(L_p(0,T)\) stability and semidiscrete error estimates for the Volterra formulation of the linear quasistatic viscoelasticity problem
• The random walk's guide to anomalous diffusion: A fractional dynamics approach