Finite Difference Schemes for the "Parabolic" Equation in a Variable Depth Environment with a Rigid Bottom Boundary Condition

DOI10.1137/S0036142999367460zbMath1005.65094MaRDI QIDQ2719221

Georgios E. Zouraris, Georgios D. Akrivis, Vassilios A. Dougalis

Publication date: 21 June 2001

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

error bound underwater acoustics variable domain problems parabolic approximations Schrödinger evolution equation Crank-Nicolson-type finite difference approximation finite difference error estimates

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Hydro- and aero-acoustics (76Q05) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (7)

The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation ⋮ Discontinuous Galerkin methods for the linear Schrödinger equation in non-cylindrical domains ⋮ Computing a numerical solution of two dimensional non-linear Schrödinger equation on complexly shaped domains by RBF based differential quadrature method ⋮ Approximating the nonlinear Schrödinger equation by a two level linearly implicit finite element method ⋮ A finite difference method for the wide-angle “parabolic” equation in a waveguide with downsloping bottom ⋮ Crank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain ⋮ Galerkin methods for a Schrödinger-type equation with a dynamical boundary condition in two dimensions

This page was built for publication: Finite Difference Schemes for the "Parabolic" Equation in a Variable Depth Environment with a Rigid Bottom Boundary Condition