Numerical solutions of viscoelastic bending wave equations with two term time kernels by Runge-Kutta convolution quadrature

DOI10.3934/dcdsb.2017122zbMath1361.65106OpenAlexW2601792187MaRDI QIDQ521509

Da Xu

Publication date: 11 April 2017

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2017122

zbMATH Keywords

stabilityconvergenceerror estimatesnumerical experimentsRunge-Kutta methodsfinite differenceinitial boundary value problemconvolution quadratureviscoelastic bending wave equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) (74C05) Finite difference methods applied to problems in solid mechanics (74S20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized convolution quadrature based on Runge-Kutta methods
• On finite difference methods for fourth-order fractional diffusion-wave and subdiffusion systems
• Runge-Kutta convolution quadrature for operators arising in wave propagation
• An error analysis of Runge-Kutta convolution quadrature
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• Stability of the difference type methods for linear Volterra equations in Hilbert spaces
• Numerical solution via Laplace transforms of a fractional order evolution equation
• 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
• Uniform \(L^1\) error bounds for the semidiscrete solution of a Volterra equation with completely monotonic convolution kernel
• Runge-Kutta time discretizations of parabolic Volterra integro- differential equations
• A compact finite difference scheme for the fourth-order fractional diffusion-wave system
• The time discretization in classes of integro-differential equations with completely monotonic kernels: weighted asymptotic stability
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Runge-Kutta convolution quadrature methods for well-posed equations with memory
• Uniform l1 behaviour for time discretization of a Volterra equation with completely monotonic kernel: I. stability
• Well-posedness of hp-version discontinuous Galerkin methods for fractional diffusion wave equations
• Discontinuous Galerkin method for an evolution equation with a memory term of positive type
• Uniform l1 behaviour in a second-order difference-type method for a linear Volterra equation with completely monotonic kernel I: stability
• Solving Ordinary Differential Equations I
• Uniform $L^1 $ Behavior in Classes of Integrodifferential Equations with Completely Monotonic Kernels
• A Difference Scheme for a Nonlinear Partial Integrodifferential Equation
• Uniform $l^{1}$ Behavior for Time Discretization of a Volterra Equation with Completely Monotonic Kernel II: Convergence
• Alternating Direction Implicit Orthogonal Spline Collocation Methods for an Evolution Equation with a Positive-Type Memory Term
• A Numerical Method for a Partial Integro-Differential Equation
• Uniform $L^1 $ Behavior for the Solution of a Volterra Equation with a Parameter
• Resolvent Formulas for a Volterra Equation in Hilbert Space
• Orthogonal Spline Collocation Methods for Some Partial Integrodifferential Equations
• A Nonhomogeneous Integrodifferential Equation in Hilbert Space
• Uniform 𝐿¹ behavior in a class of linear Volterra equations
• Numerical solution of an evolution equation with a positive-type memory term
• Spline Collocation Methods for a Class of Hyperbolic Partial Integro-Differential Equations
• Spectral collocation methods for a partial integro-differential equation with a weakly singular kernel
• Complete Monotonicity and Resolvents of Volterra Integrodifferential Equations
• Time discretization of an evolution equation via Laplace transforms
• Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term
• Superconvergence of a Discontinuous Galerkin Method for Fractional Diffusion and Wave Equations
• The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-differential Equation with a Weakly Singular Kernel
• Numerical solution of evolutionary integral equations with completely monotonic kernel by Runge–Kutta convolution quadrature
• Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation
• Indirect Abelian Theorems and a Linear Volterra Equation