Theoretical analysis of a conservative finite-difference scheme to solve a Riesz space-fractional Gross-Pitaevskii system
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Publication:2059607
DOI10.1016/j.cam.2021.113413zbMath1486.65129OpenAlexW3124001662MaRDI QIDQ2059607
Adán J. Serna-Reyes, Jorge Eduardo Macías-Díaz
Publication date: 14 December 2021
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2021.113413
convergence analysisstability analysisconservation of energyRiesz space-fractional derivativesfractional Gross-Pitaevskii system
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) Fractional partial differential equations (35R11)
Related Items (4)
CMMSE: analysis and comparison of some numerical methods to solve a nonlinear fractional Gross-Pitaevskii system ⋮ A nonlinear discrete model for approximating a conservative multi-fractional Zakharov system: analysis and computational simulations ⋮ A stable and convergent finite-difference model which conserves the positivity and the dissipativity of Gibbs' free energy for a nonlinear combustion equation ⋮ Analysis of a scheme which preserves the dissipation and positivity of Gibbs' energy for a nonlinear parabolic equation with variable diffusion
Cites Work
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- Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations
- Analysis of a meshless method for the time fractional diffusion-wave equation
- A new difference scheme for the time fractional diffusion equation
- A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain
- The discrete variational derivative method based on discrete differential forms
- On the transmission of binary bits in discrete Josephson-junction arrays
- 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
- Two energy conserving numerical schemes for the sine-Gordon equation
- On the propagation of binary signals in damped mechanical systems of oscillators
- 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 structure-preserving method for a class of nonlinear dissipative wave equations with Riesz space-fractional derivatives
- Exact energy and momentum conserving algorithms for general models in nonlinear elasticity
- Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations.
- Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation
- Persistence of nonlinear hysteresis in fractional models of Josephson transmission lines
- 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
- 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
- Two finite difference schemes for time fractional diffusion-wave equation
- An alternating discrete variational derivative method for coupled partial differential equations
- 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
- A numerical method with properties of consistency in the energy domain for a class of dissipative nonlinear wave equations with applications to a Dirichlet boundary-value problem
- The Fractional Order Fourier Transform and its Application to Quantum Mechanics
- A new energy and momentum conserving algorithm for the non‐linear dynamics of shells
- 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
- On the solution of a Riesz space-fractional nonlinear wave equation through an efficient and energy-invariant scheme
- Symplectic methods for the nonlinear Schrödinger 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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