A Crank-Nicolson-type finite-difference scheme and its algorithm implementation for a nonlinear partial integro-differential equation arising from viscoelasticity

DOI10.1007/s40314-020-01337-xzbMath1476.65352OpenAlexW3092883696WikidataQ114219337 ScholiaQ114219337MaRDI QIDQ1983786

Xuan Zheng, Wenlin Qiu, Hong-Bin Chen

Publication date: 10 September 2021

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-020-01337-x

zbMATH Keywords

numerical experimentnumerical algorithmconvolution quadraturestability and convergencenonlinear partial integro-differential equationCrank-Nicolson-type finite-difference scheme

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (6)

A predictor-corrector compact finite difference scheme for a nonlinear partial integro-differential equation ⋮ A novel hybrid approach for computing numerical solution of the time-fractional nonlinear one and two-dimensional partial integro-differential equation ⋮ Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation ⋮ An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation ⋮ Second-order accurate numerical scheme with graded meshes for the nonlinear partial integrodifferential equation arising from 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
• A parallel-in-time iterative algorithm for Volterra partial integro-differential problems with weakly singular kernel
• Approximation of a circular cylindrical shell by Clough-Johnson flat plate finite elements
• A finite difference scheme for partial integro-differential equations with a weakly singular kernel
• The global behavior of time discretization for an abstract Volterra equation in Hilbert space
• A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations
• A fractional trapezoidal rule for integro-differential equations of fractional order in Banach spaces
• Optimal convergence of an Euler and finite difference method for nonlinear partial integro-differential equations
• A linear finite difference scheme for generalized time fractional Burgers equation
• Crank-Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation
• Error estimate of finite element/finite difference technique for solution of two-dimensional weakly singular integro-partial differential equation with space and time fractional derivatives
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• Discretized Fractional Calculus
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the First Kind
• Error Estimates of Crank–Nicolson-Type Difference Schemes for the Subdiffusion Equation
• Solution of a partial integro-differential equation arising from viscoelasticity
• An alternating direction implicit fractional trapezoidal rule type difference scheme for the two-dimensional fractional evolution equation
• A Difference Scheme for a Nonlinear Partial Integrodifferential Equation
• Bifurcation with Memory
• Time Discretization of an Integro-Differential Equation of Parabolic Type
• A Numerical Method for a Partial Integro-Differential Equation
• On two linearized difference schemes for Burgers’ equation
• A second-order BDF compact difference scheme for fractional-order Volterra equation

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