Fractional generalization of the Fermi-Pasta-Ulam-Tsingou media and theoretical analysis of an explicit variational scheme

DOI10.1016/j.cnsns.2019.105158zbMath1452.65202OpenAlexW3013680866MaRDI QIDQ2208082

Jorge Eduardo Macías-Díaz

Publication date: 23 October 2020

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

Full work available at URL: https://doi.org/10.1016/j.cnsns.2019.105158

zbMATH Keywords

energy-preserving methodfractional centered differencesRiesz space-fractional equationsnumerical efficiency analysisconservative fractional wave equationcontinuous Fermi-Pasta-Ulam-Tsingou media

Mathematics Subject Classification ID

Statistical mechanics of crystals (82D25) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (2)

A nonlinear discrete model for approximating a conservative multi-fractional Zakharov system: analysis and computational simulations ⋮ Fast dissipation-preserving difference scheme for nonlinear generalized wave equations with the integral fractional Laplacian

Cites Work

• Unnamed Item
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• Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations
• A new difference scheme for the time fractional diffusion equation
• Approximate analytical solution of the nonlinear fractional KdV-Burgers equation: a new iterative algorithm
• An energy conservative difference scheme for the nonlinear fractional Schrödinger equations
• A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain
• A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
• The discrete variational derivative method based on discrete differential forms
• Fractional Pais-Uhlenbeck oscillator
• Fractional dynamics of populations
• An implicit four-step computational method in the study on the effects of damping in a modified Fermi-Pasta-Ulam medium
• Conservation laws and Hamilton's equations for systems with long-range interaction and memory
• A computational technique with multiple properties of consistency in the study of modified \(\beta \)-Fermi-Pasta-Ulam chains
• Numerical solution of a nonlinear wave equation in polar coordinates
• Two energy conserving numerical schemes for the sine-Gordon equation
• Riesz potential operators and inverses via fractional centred derivatives
• GENERIC formalism and discrete variational derivative method for the two-dimensional vorticity equation
• Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations
• Numerical solution of the sine-Gordon equation
• Numerical solution of a nonlinear Klein-Gordon equation
• A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation
• Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations.
• Sufficient conditions for the preservation of the boundedness in a numerical method for a physical model with transport memory and nonlinear damping
• Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives
• Numerical simulation of the nonlinear dynamics of harmonically driven Riesz-fractional extensions of the Fermi-Pasta-Ulam chains
• An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions
• Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions
• Supratransmission in \(\beta\)-Fermi-Pasta-Ulam chains with different ranges of interactions
• Some energy preserving finite element schemes based on the discrete variational derivative method
• Numerical simulation for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method
• An alternating discrete variational derivative method for coupled partial differential equations
• Fractional heat equation and the second law of thermodynamics
• An explicit finite-difference method for the approximate solutions of a generic class of anharmonic dissipative nonlinear media
• Application of the variational principle to deriving energy-preserving schemes for the Hamilton equation
• A novel discrete variational derivative method using ``average-difference methods
• Applications of Fractional Calculus to the Theory of Viscoelasticity
• Continuous limit of discrete systems with long-range interaction
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• DESIGN OF ENERGY CONSERVING ALGORITHMS FOR FRICTIONLESS DYNAMIC CONTACT PROBLEMS
• An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics
• Long way from the FPU-problem to chaos
• Symplectic methods for the nonlinear Schrödinger equation
• A stable and conservative finite difference scheme for the Cahn-Hilliard equation
• Finite-difference schemes for nonlinear wave equation that inherit energy conservation property
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

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