Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium
DOI10.3934/era.2020079zbMath1458.65134OpenAlexW3046915531MaRDI QIDQ2220676
Publication date: 25 January 2021
Published in: Electronic Research Archive (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/era.2020079
finite difference methoditerative methodnonlinear Helmholtz equationKerr mediumdiscontinuous coefficient problem
Iterative procedures involving nonlinear operators (47J25) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Numerical solutions to equations with nonlinear operators (65J15) Finite difference methods for boundary value problems involving PDEs (65N06)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Error correction method for Navier-Stokes equations at high Reynolds numbers
- The nonlinear Schrödinger equation. Singular solutions and optical collapse
- Oscillating solutions for nonlinear Helmholtz equations
- High-order numerical solution of the nonlinear Helmholtz equation with axial symmetry
- A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media
- A new method to deduce high-order compact difference schemes for two-dimensional Poisson equation
- Robust iterative method for nonlinear Helmholtz equation
- Energy stable discontinuous Galerkin methods for Maxwell's equations in nonlinear optical media
- A family of fourth-order and sixth-order compact difference schemes for the three-dimensional Poisson equation
- Dual variational methods and nonvanishing for the nonlinear Helmholtz equation
- High-order numerical method for the nonlinear Helmholtz equation with material discontinuities in one space dimension
- Numerical solution of the nonlinear Helmholtz equation using nonorthogonal expansions
- Existence and asymptotic behavior of standing waves of the nonlinear Helmholtz equation in the plane
- Compact ADI method for solving parabolic differential equations
- Finite Element Method and its Analysis for a Nonlinear Helmholtz Equation with High Wave Numbers
- Uniformly convergent novel finite difference methods for singularly perturbed reaction–diffusion equations
- Efficient and Accurate Numerical Solutions for Helmholtz Equation in Polar and Spherical Coordinates
- High-order two-way artificial boundary conditions for nonlinear wave propagation with backscattering
This page was built for publication: Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium