Stable and convergent difference schemes for weakly singular convolution integrals

DOI10.1216/JIE.2021.33.271OpenAlexW4213203814WikidataQ114060207 ScholiaQ114060207MaRDI QIDQ2146556

Richard D. Noren, Wesley Davis

Publication date: 16 June 2022

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/jie.2021.33.271

zbMATH Keywords

integral equationsnumerical convergencefractional derivativenumerical analysiscomposite quadrature

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Fractional derivatives and integrals (26A33) Volterra integral equations (45D05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Cites Work

• Finite difference methods for the time fractional diffusion equation on non-uniform meshes
• Convolution quadrature and discretized operational calculus. I
• Convolution quadrature and discretized operational calculus. II
• Nonlinearly perturbed Volterra equations
• On convolution quadrature and Hille-Phillips operational calculus
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• A fully discrete difference scheme for a diffusion-wave system
• Convergence and stability of quadrature methods applied to Volterra equations with delay
• An Introduction to Numerical Analysis
• Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Volterra Integral Equations in Banach Space
• Monotonicity of Solutions of Volterra Integral Equations in Banach Space
• Linear integral equations
• A C^α finite difference method for the Caputo time‐fractional diffusion equation

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