Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the sinc-collocation method based on the double exponential transformation

DOI10.1016/J.AMC.2020.125693zbMath1488.65753OpenAlexW3092269795WikidataQ112880132 ScholiaQ112880132MaRDI QIDQ2662538

Wenlin Qiu, Jing Guo, Da Xu

Publication date: 14 April 2021

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

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125693

zbMATH Keywords

convergence analysissinc-collocation methoddouble exponential transformationmulti-term kernelsfourth-order partial integro-differential equation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items (17)

A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation ⋮ A formally second‐order <scp>backward differentiation formula</scp> Sinc‐collocation method for the Volterra integro‐differential equation with a weakly singular kernel based on the double exponential transformation ⋮ ROBUST IMPLICIT DIFFERENCE APPROACH FOR THE TIME-FRACTIONAL KURAMOTO–SIVASHINSKY EQUATION WITH THE NON-SMOOTH SOLUTION ⋮ Optimal error estimate of an accurate second-order scheme for Volterra integrodifferential equations with tempered multi-term kernels ⋮ The finite difference method for the fourth‐order partial integro‐differential equations with the multi‐term weakly singular kernel ⋮ On existence and numerical solution of higher order nonlinear integro-differential equations involving variable coefficients ⋮ Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion ⋮ An implicit difference scheme for the fourth-order nonlinear partial integro-differential equations ⋮ An efficient parametric finite difference and orthogonal spline approximation for solving the weakly singular nonlinear time-fractional partial integro-differential equation ⋮ An operator splitting method for multi-asset options with the Feynman-Kac formula ⋮ Unnamed Item ⋮ A Crank-Nicolson-type compact difference method with the uniform time step for a class of weakly singular parabolic integro-differential equations ⋮ A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels ⋮ ADI Galerkin finite element scheme for the two-dimensional semilinear partial intergro-differential equation with a weakly singular kernel ⋮ Orthogonal spline collocation method for the two-dimensional time fractional mobile-immobile equation ⋮ A spectral order method for solving the nonlinear fourth-order time-fractional problem ⋮ Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: stability analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximum principle for the multi-term time-fractional diffusion equations with the Riemann-Liouville fractional derivatives
• Sinc-Galerkin and sinc-collocation methods in the solution of nonlinear two-point boundary value problems
• Double exponential transformation in the sinc-collocation method for a boundary value problem with fourth-order ordinary differential equation
• A high-order numerical method for solving the 2D fourth-order reaction-diffusion equation
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• Convolution quadrature and discretized operational calculus. I
• Uniform \(L^ 1\) behavior in classes of integrodifferential equations with convex kernels
• 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
• Optimality of the double exponential formula -- functional analysis approach
• Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method
• Numerical asymptotic stability for the integro-differential equations with the multi-term kernels
• The time discretization in classes of integro-differential equations with completely monotonic kernels: weighted asymptotic stability
• An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations
• BDF ADI orthogonal spline collocation scheme for the fractional integro-differential equation with two weakly singular kernels
• Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction-diffusion problem
• A two-grid mixed finite element method for a nonlinear fourth-order reaction-diffusion problem with time-fractional derivative
• A spline collocation method for a fractional mobile-immobile equation with variable coefficients
• A time two-grid algorithm based on finite difference method for the two-dimensional nonlinear time-fractional mobile/immobile transport model
• Numerical solution of variable-order fractional integro-partial differential equations via sinc collocation method based on single and double exponential transformations
• The finite volume scheme preserving maximum principle for two-dimensional time-fractional Fokker-Planck equations on distorted meshes
• An alternating direction implicit orthogonal spline collocation method for the two dimensional multi-term time fractional integro-differential equation
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Solution of a Volterra integral equation by the sinc-collocation method
• A second-order accurate numerical method with graded meshes for an evolution equation with a weakly singular kernel
• The double exponential sinc collocation method for singular Sturm-Liouville problems
• The time discretization in classes of integro-differential equations with completely monotonic kernels: Weighted asymptotic convergence
• Discretized Fractional Calculus
• Function classes for successful DE-Sinc approximations
• Uniform $L^1 $ Behavior in Classes of Integrodifferential Equations with Completely Monotonic Kernels
• Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
• The Sinc-Galerkin Method for Fourth-Order Differential Equations
• A "Sinc-Galerkin" Method of Solution of Boundary Value Problems
• Near optimality of the sinc approximation
• Convergence of the Sinc Method for a Fourth-Order Ordinary Differential Equation with an Application
• A backward Euler difference scheme for the integro-differential equations with the multi-term kernels
• A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels
• Inequalities: theory of majorization and its applications

This page was built for publication: Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the sinc-collocation method based on the double exponential transformation