Energy-conserving SAV-Hermite-Galerkin spectral scheme with time adaptive method for coupled nonlinear Klein-Gordon system in multi-dimensional unbounded domains
DOI10.1016/j.cam.2024.116204zbMATH Open1547.65154MaRDI QIDQ6593356
Xiaohao Zhang, Shimin Guo, Liquan Mei
Publication date: 26 August 2024
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
KdV equations (Korteweg-de Vries equations) (35Q53) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Error estimates in the energy space for a Gautschi-type integrator spectral discretization for the coupled nonlinear Klein-Gordon equations
- Laguerre spectral approximation of elliptic problems in exterior domains
- Weak solutions for a system of nonlinear Klein-Gordon equations
- Numerical solution of a nonlinear Klein-Gordon equation
- Vlasov simulations using velocity-scaled Hermite representations
- Fourier collocation method for solving nonlinear Klein-Gordon equation
- The numerical computation of connecting orbits in dynamical systems: A rational spectral approach
- Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval
- The scalar auxiliary variable (SAV) approach for gradient flows
- The use of generalized Laguerre polynomials in spectral methods for nonlinear differential equations
- Spectral methods using rational basis functions on an infinite interval
- On a mixed problem for a class of nonlinear Klein-Gordon equations
- Soliton solutions of coupled nonlinear Klein--Gordon equations
- A trigonometric integrator pseudospectral discretization for the \(N\)-coupled nonlinear Klein-Gordon equations
- Highly efficient and accurate numerical schemes for the epitaxial thin film growth models by using the SAV approach
- Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis
- Dissipation-preserving rational spectral-Galerkin method for strongly damped nonlinear wave system involving mixed fractional Laplacians in unbounded domains
- Energy-conserving and time-stepping-varying ESAV-Hermite-Galerkin spectral scheme for nonlocal Klein-Gordon-Schrödinger system with fractional Laplacian in unbounded domains
- A new Lagrange multiplier approach for gradient flows
- Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable
- Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
- Energy conserving discontinuous Galerkin method with scalar auxiliary variable technique for the nonlinear Dirac equation
- Spectral Methods
- An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
- Combined Hermite spectral-finite difference method for the Fokker-Planck equation
- Non-existence of global solutions of a class of coupled non-linear Klein-Gordon equations with non-negative potentials and arbitrary initial energy
- Product Approximation for Nonlinear Klein-Gordon Equations
- Approximation of Some Diffusion Evolution Equations in Unbounded Domains by Hermite Functions
- Modified Hermite polynomials in the spectral approximation for boundary layer problems
- Solitary Wave Collisions
- Error estimation of Hermite spectral method for nonlinear partial differential equations
- Nystroem interpolants based on zeros of Laguerre polynomials for some Weiner-Hopf equations
- Sympletic Finite Difference Approximations of the Nonlinear Klein--Gordon Equation
- Stable and Efficient Spectral Methods in Unbounded Domains Using Laguerre Functions
- Hermite pseudospectral method for nonlinear partial differential equations
- An Adaptive Time-Stepping Strategy for the Cahn-Hilliard Equation
- A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation
- On the standing wave in coupled non-linear Klein-Gordon equations
- Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
- High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
- Implicit-explicit relaxation Runge-Kutta methods: construction, analysis and applications to PDEs
- A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows
- A Uniformly Accurate Multiscale Time Integrator Pseudospectral Method for the Klein--Gordon Equation in the Nonrelativistic Limit Regime
- Conservative compact finite difference scheme for the N‐coupled nonlinear Klein–Gordon equations
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Parameter-Free Time Adaptivity Based on Energy Evolution for the Cahn-Hilliard Equation
- A rational approximation and its applications to differential equations on the half line
- Relaxation Exponential Rosenbrock-Type Methods for Oscillatory Hamiltonian Systems
- A space-time spectral method for solving the nonlinear Klein-Gordon equation
This page was built for publication: Energy-conserving SAV-Hermite-Galerkin spectral scheme with time adaptive method for coupled nonlinear Klein-Gordon system in multi-dimensional unbounded domains