An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy

DOI10.1016/j.apnum.2021.06.014zbMath1475.35321OpenAlexW3180263986MaRDI QIDQ2048432

Jorge Eduardo Macías-Díaz, Romeo Martínez, Qin Sheng

Publication date: 5 August 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.06.014

zbMATH Keywords

conservation of energyRiesz space-fractional equationsenergy-conserving methodnumerical efficiency analysisfractional-order centered differencesfractional-order Klein-Gordon-Zakharov equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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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 fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• Optimal existence and uniqueness theory for the fractional heat equation
• A fractional porous medium equation
• Recent history of fractional calculus
• A fourth-order approximation of fractional derivatives with its applications
• Two energy conserving numerical schemes for the sine-Gordon equation
• Derivation of the Zakharov equations
• Riesz potential operators and inverses via fractional centred derivatives
• From a generalised Helmholtz decomposition theorem to fractional Maxwell equations
• Fractional vector calculus and fractional Maxwell's equations
• A boundedness-preserving finite-difference scheme for a damped nonlinear wave equation
• From the Klein-Gordon-Zakharov system to a singular nonlinear Schrödinger system
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• New exact traveling wave solutions for the Klein-Gordon-Zakharov equations
• Numerical solution of the sine-Gordon equation
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach
• A review of applications of fractional calculus in Earth system dynamics
• A review of definitions for fractional derivatives and integral
• Existence and blowup of solutions for the modified Klein-Gordon-Zakharov equations for plasmas with a quantum correction
• The differentiability in the fractional calculus.
• Normal form and global solutions for the Klein-Gordon-Zakharov equations
• On a fractional thin film equation
• The role of fractional calculus in modeling biological phenomena: a review
• A high-order \(L2\)-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients
• An energy-preserving and efficient scheme for a double-fractional conservative Klein-Gordon-Zakharov system
• An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions
• A numerically efficient and conservative model for a Riesz space-fractional Klein-Gordon-Zakharov system
• Corrigendum to: ``A numerically efficient and conservative model for a Riesz space-fractional Klein-Gordon-Zakharov system
• Supratransmission in \(\beta\)-Fermi-Pasta-Ulam chains with different ranges of interactions
• A new collection of real world applications of fractional calculus in science and engineering
• Classical solutions and higher regularity for nonlinear fractional diffusion equations
• A spatially sixth-order hybrid \(L1\)-CCD method for solving time fractional Schrödinger equations.
• ON THE RIEMANN-LIOUVILLE FRACTIONAL CALCULUS AND SOME RECENT APPLICATIONS
• FROM THE KLEIN–GORDON–ZAKHAROV SYSTEM TO THE NONLINEAR SCHRÖDINGER EQUATION
• Continuous limit of discrete systems with long-range interaction
• The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation
• A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
• Interprétation géométrique de la différentiabilité et du gradient d'ordre réel
• Global smooth solution for the Klein–Gordon–Zakharov equations
• Fourth-order methods for space fractional reaction–diffusion equations with non-smooth data
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• The Fisher-KPP Equation with Nonlinear Fractional Diffusion
• A class of second order difference approximations for solving space fractional diffusion equations
• Symplectic methods for the nonlinear Schrödinger equation