Numerical analysis and simulation for a nonlinear wave equation

DOI10.1016/J.CAM.2015.09.024zbMath1331.65142OpenAlexW1772423227MaRDI QIDQ898951

N. P. Quintino, M. A. Rincon

Publication date: 21 December 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.09.024

zbMATH Keywords

Newton's methodnumerical examplesblow-uperror estimatenonlinear wave equationfinite difference method in timefinite element method in the spatial variable

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (10)

A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations ⋮ A numerical algorithm for the nonlinear Timoshenko beam system ⋮ Efficient and accurate numerical methods for nonlinear strongly damped wave equation in 2+1 dimensions ⋮ Unconditional superconvergence analysis of a linearized Galerkin FEM for nonlinear hyperbolic equations ⋮ On the \(L^{\infty}\)-convergence of two conservative finite difference schemes for fourth-order nonlinear strain wave equations ⋮ On a nonlinear problem with Dirichlet and acoustic boundary conditions ⋮ Theoretical analysis and numerical simulation for a hyperbolic equation with Dirichlet and acoustic boundary conditions ⋮ Numerical analysis and simulation for a wave equation with dynamical boundary control ⋮ A finite element scheme for a 2D-wave equation with dynamical boundary control ⋮ A new approach to convergence analysis of linearized finite element method for nonlinear hyperbolic equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string
• Numerical studies of the damped Korteweg-de Vries system
• Blow-up theorems for nonlinear wave equations
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• Galerkin Methods for Parabolic Equations
• $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations
• $L_\infty $ Estimates of Optimal Orders for Galerkin Methods for One-Dimensional Second Order Parabolic and Hyperbolic Equations

This page was built for publication: Numerical analysis and simulation for a nonlinear wave equation