The Crank-Nicolson finite element method for the 2D uniform transmission line equation

DOI10.1186/s13660-020-02370-4zbMath1503.65183OpenAlexW3028748908MaRDI QIDQ2069394

Yiting Fan, Hulin Ren, Zhen-Dong Luo

Publication date: 20 January 2022

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-020-02370-4

zbMATH Keywords

error estimatenumerical testuniform transmission line equationCrank-Nicolson finite element methodstability and existence

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Cites Work

• Unnamed Item
• Unnamed Item
• A numerical study of two dimensional hyperbolic telegraph equation by modified B-spline differential quadrature method
• A new spectral Galerkin method for solving the two dimensional hyperbolic telegraph equation
• A meshless collocation approach with barycentric rational interpolation for two-dimensional hyperbolic telegraph equation
• A Crank-Nicolson collocation spectral method for the two-dimensional telegraph equations
• A reduced-order extrapolated Crank-Nicolson finite spectral element method based on POD for the 2D non-stationary Boussinesq equations
• A new method for solving the hyperbolic telegraph equation
• A reduced-order extrapolated Crank-Nicolson finite spectral element method for the 2D non-stationary Navier-Stokes equations about vorticity-stream functions
• A reduced-order extrapolating collocation spectral method based on POD for the 2D Sobolev equations
• A reduced order extrapolating technique of solution coefficient vectors to collocation spectral method for telegraph equation
• A highly efficient reduced-order extrapolated finite difference algorithm for time-space tempered fractional diffusion-wave equation
• A reduced-order extrapolation technique for solution coefficient vectors in the mixed finite element method for the 2D nonlinear Rosenau equation
• A reduced-order extrapolated natural boundary element method based on POD for the parabolic equation in the 2D unbounded domain
• Numerical approximation of higher-order time-fractional telegraph equation by using a combination of a geometric approach and method of line
• Proper orthogonal decomposition reduced-order extrapolation continuous space-time finite element method for the two-dimensional unsteady Stokes equation
• High-order numerical solution of second-order one-dimensional hyperbolic telegraph equation using a shifted Gegenbauer pseudospectral method
• A reduced‐order extrapolated Crank–Nicolson collocation spectral method based on proper orthogonal decomposition for the two‐dimensional viscoelastic wave equations
• The Crank–Nicolson finite spectral element method and numerical simulations for 2D non‐stationary Navier–Stokes equations
• A reduced‐order extrapolated natural boundary element method based on POD for the 2D hyperbolic equation in unbounded domain
• New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations