Stability and Error Analysis for a Second-Order Fast Approximation of the Local and Nonlocal Diffusion Equations on the Real Line

DOI10.1137/19M1285822zbMath1446.82045MaRDI QIDQ3303718

Chunxiong Zheng, Qiang Du, Jiwei Zhang, Xiang Ma

Publication date: 4 August 2020

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

zbMATH Keywords

fast algorithmabsorbing boundary conditionsartificial boundary methodnonlocal diffusion equationstability and error analysisasymptotically compatibleDtN-type map

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Dynamic continuum models (systems of particles, etc.) in time-dependent statistical mechanics (82C21) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Linear integral equations (45A05) Applications of functional analysis to differential and integral equations (46N20)

Related Items (11)

A Dual-Horizon Nonlocal Diffusion Model and Its Finite Element Discretization ⋮ Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation ⋮ A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system ⋮ Space reduction for linear systems with local symmetry ⋮ Two SAV numerical methods for the nonlocal Cahn-Hilliard-Hele-Shaw system ⋮ A fast accurate artificial boundary condition for the Euler-Bernoulli beam ⋮ Accurate Absorbing Boundary Conditions for the Two-Dimensional Nonlocal Schrödinger Equations ⋮ Construction and analysis of discretization schemes for one-dimensional nonlocal Schrödinger equations with exact absorbing boundary conditions ⋮ Fast artificial boundary method for the heat equation on unbounded domains with strip tails ⋮ Numerical solutions for nonlocal wave equations by perfectly matched layers. II: The two-dimensional case ⋮ A stable and high-order numerical scheme with discrete DtN-type artificial boundary conditions for a 2D peridynamic diffusion model

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