Efficient simulation of complex Ginzburg-Landau equations using high-order exponential-type methods

Numerical methods for ordinary differential equations (65Lxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Partial differential equations of mathematical physics and other areas of application (35Qxx)

Cites Work

Unnamed Item
An efficient split-step compact finite difference method for cubic-quintic complex Ginzburg-Landau equations
An efficient Chebyshev-tau spectral method for Ginzburg-Landau-Schrödinger equations
Lattice Boltzmann simulations for the vortex tori pattern in the three-dimensional cubic-quintic complex Ginzburg-Landau equation
Existence and decay estimates of solutions to complex Ginzburg-Landau type equations
High-order time-splitting Hermite and Fourier spectral methods
Splitting methods with complex times for parabolic equations
High order splitting methods for analytic semigroups exist
On-the-fly backward error estimate for matrix exponential approximation by Taylor algorithm
Mathematical theory and numerical methods for Bose-Einstein condensation
Solving periodic semilinear stiff PDEs in 1D, 2D and 3D with exponential integrators
Boosting the computation of the matrix exponential
Exponential methods for solving hyperbolic problems with application to collisionless kinetic equations
A low-rank Lie-Trotter splitting approach for nonlinear fractional complex Ginzburg-Landau equations
A \(\mu\)-mode integrator for solving evolution equations in Kronecker form
Multidimensional dissipative solitons and solitary vortices
A \(\mu\)-mode BLAS approach for multidimensional tensor-structured problems
Convergence of a splitting method of high order for reaction-diffusion systems
The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
Exponential integrators
The world of the complex Ginzburg-Landau equation
A New Scaling and Squaring Algorithm for the Matrix Exponential
High-order time-splitting methods for irreversible equations
Global existence and uniqueness of solutions of the time-dependent ginzburg-landau model for superconductivity
High Order Exponential Integrators for Nonlinear Schrödinger Equations with Application to Rotating Bose--Einstein Condensates
Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation
A non-linear instability theory for a wave system in plane Poiseuille flow
Generalized Runge-Kutta Processes for Stable Systems with Large Lipschitz Constants
Unconditionally convergent and superconvergent analysis of second-order weighted IMEX FEMs for nonlinear Ginzburg-Landau equation
Preconditioned fourth-order exponential integrator for two-dimensional nonlinear fractional Ginzburg-Landau equation
Performance of affine-splitting pseudo-spectral methods for fractional complex Ginzburg-Landau equations
Accelerating Exponential Integrators to Efficiently Solve Semilinear Advection-Diffusion-Reaction Equations
Euler polynomials for the matrix exponential approximation
A second order directional split exponential integrator for systems of advection-diffusion-reaction equations

This page was built for publication: Efficient simulation of complex Ginzburg-Landau equations using high-order exponential-type methods