Uniform $l^1$ Behavior of a Time Discretization Method for a Volterra Integrodifferential Equation with Convex Kernel; Stability

DOI10.1137/100804656zbMath1230.65141OpenAlexW2003420214MaRDI QIDQ3097470

Richard D. Noren, Charles B. Harris

Publication date: 10 November 2011

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/100804656

zbMATH Keywords

Fourier transformLaplace transformbackward Euler methodconvolution quadratureVolterra integrodifferential equationtime discretization methodconvex kernel\(l^1\)-stability

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Volterra integral equations (45D05)

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Strong order of convergence of a fully discrete approximation of a linear stochastic Volterra type evolution equation ⋮ The long time error analysis in the second order difference type method of an evolutionary integral equation with completely monotonic kernel ⋮ Asymptotics and discretization of a weakly singular kernel: application to viscous flows in a network of thin tubes ⋮ The time discretization in classes of integro-differential equations with completely monotonic kernels: weighted asymptotic stability ⋮ Uniform \(l^1\) behavior in the Crank-Nicolson methods for a linear Volterra equation with convex kernel ⋮ The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence ⋮ Decay properties for the numerical solutions of a partial differential equation with memory

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