Improved uniform error bounds for long-time dynamics of the high-dimensional nonlinear space fractional sine-Gordon equation with weak nonlinearity

DOI10.1016/J.CAMWA.2024.09.001MaRDI QIDQ6663361

Junqing Jia, X. Jiang, Xiaoqing Chi

Publication date: 14 January 2025

Published in: Computers & Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

long-time dynamicstime-splitting methodimproved uniform error boundsregularity compensation oscillationnonlinear space fractional sine-Gordon equation

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• Title not available (Why is that?)
• Numerical simulation of two-dimensional sine-Gordon solitons via a local weak meshless technique based on the radial point interpolation method (RPIM)
• Non-standard extensions of gradient elasticity: fractional non-locality, memory and fractality
• Long-time existence for semi-linear Klein-Gordon equations on tori
• High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods
• A high order compact time/space finite difference scheme for the wave equation with variable speed of sound
• Numerical solutions of a damped sine-Gordon equation in two space variables
• Numerical simulation of two-dimensional sine-Gordon solitons by differential quadrature method
• Numerical study of the process of nonlinear supratransmission in Riesz space-fractional sine-Gordon equations
• Compact difference scheme for a class of fractional-in-space nonlinear damped wave equations in two space dimensions
• Mass-conservative Fourier spectral methods for solving the fractional nonlinear Schrödinger equation
• Energy-preserving time high-order AVF compact finite difference schemes for nonlinear wave equations with variable coefficients
• Numerical investigation of fractional nonlinear sine-Gordon and Klein-Gordon models arising in relativistic quantum mechanics
• Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
• What is the fractional Laplacian? A comparative review with new results
• A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations
• A linearly implicit structure-preserving scheme for the fractional sine-Gordon equation based on the IEQ approach
• A linearly implicit and local energy-preserving scheme for the sine-Gordon equation based on the invariant energy quadratization approach
• Error analysis and numerical simulations of Strang splitting method for space fractional nonlinear Schrödinger equation
• Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers
• Coupled oscillators with power-law interaction and their fractional dynamics analogues
• Nonlinear stability of 2-solitons of the sine-Gordon equation in the energy space
• The sine-Gordon model and its applications. From pendula and Josephson junctions to gravity and high-energy physics
• Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions
• The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations
• Dissipation-preserving Fourier pseudo-spectral method for the space fractional nonlinear sine-Gordon equation with damping
• Spectral Methods
• On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
• Convergence of the interpolated coefficient finite element method for the two-dimensional elliptic sine-Gordon equations
• On time-splitting methods for nonlinear Schrödinger equation with highly oscillatory potential
• A predictor--corrector scheme for the sine-Gordon equation
• Analysis and Approximation of a Fractional Cahn--Hilliard Equation
• Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein–Gordon equation with weak nonlinearity
• Numerical discretization and fast approximation of a variably distributed-order fractional wave equation
• Improved Uniform Error Bounds on Time-Splitting Methods for Long-Time Dynamics of the Nonlinear Klein--Gordon Equation with Weak Nonlinearity
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
• Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schrödinger equation
• Improved uniform error bounds of exponential wave integrator method for long-time dynamics of the space fractional Klein-Gordon equation with weak nonlinearity
• Barycentric rational interpolation and local radial basis functions based numerical algorithms for multidimensional <scp>sine‐Gordon</scp> equation
• Long time error analysis of the fourth‐order compact finite difference methods for the nonlinear <scp>Klein–Gordon</scp> equation with weak nonlinearity
• Improved uniform error bound on the time-splitting method for the long-time dynamics of the fractional nonlinear Schrödinger equation
• Improved uniform error estimates for the two-dimensional nonlinear space fractional Dirac equation with small potentials over long-time dynamics
• Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation
• Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation

This page was built for publication: Improved uniform error bounds for long-time dynamics of the high-dimensional nonlinear space fractional sine-Gordon equation with weak nonlinearity

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6663361)