Second-order accurate numerical scheme with graded meshes for the nonlinear partial integrodifferential equation arising from viscoelasticity

DOI10.1016/j.cnsns.2022.106804OpenAlexW4221161607WikidataQ113877773 ScholiaQ113877773MaRDI QIDQ2094424

Wenlin Qiu, Xu Xiao, Kexin Li

Publication date: 28 October 2022

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.12226

zbMATH Keywords

existence and uniquenessnon-uniform meshesstability and convergencenonlinear partial integrodifferential equationsecond-order accurate difference schemeproduct-integration rule

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Numerical analysis (65-XX)

Related Items (5)

A fast numerical solution of the <scp>3D</scp> nonlinear tempered fractional integrodifferential equation ⋮ Pointwise error analysis of the BDF3 compact finite difference scheme for viscous Burgers' equations ⋮ Optimal error analysis of space-time second-order difference scheme for semi-linear non-local Sobolev-type equations with weakly singular kernel ⋮ Second-order accurate, robust and efficient ADI Galerkin technique for the three-dimensional nonlocal heat model arising in viscoelasticity ⋮ A second-order accurate Crank-Nicolson finite difference method on uniform meshes for nonlinear partial integro-differential equations with weakly singular kernels

Cites Work

• Unnamed Item
• Unnamed Item
• Finite difference methods for the time fractional diffusion equation on non-uniform meshes
• A second-order accurate numerical method for a fractional wave equation
• A finite difference scheme for partial integro-differential equations with a weakly singular kernel
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Optimal convergence of an Euler and finite difference method for nonlinear partial integro-differential equations
• A Crank-Nicolson-type finite-difference scheme and its algorithm implementation for a nonlinear partial integro-differential equation arising from viscoelasticity
• An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations
• Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
• Discontinuous Galerkin method for an evolution equation with a memory term of positive type
• Error Estimates of Crank–Nicolson-Type Difference Schemes for the Subdiffusion Equation
• Solution of a partial integro-differential equation arising from viscoelasticity
• A Difference Scheme for a Nonlinear Partial Integrodifferential Equation
• A second-order accurate numerical method for a semilinear integro-differential equation with a weakly singular kernel
• Bifurcation with Memory
• A Numerical Method for a Partial Integro-Differential Equation
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

This page was built for publication: Second-order accurate numerical scheme with graded meshes for the nonlinear partial integrodifferential equation arising from viscoelasticity