A new fourth-order numerical algorithm for a class of nonlinear wave equations

DOI10.1016/j.apnum.2012.07.004zbMath1254.65090OpenAlexW2026998301MaRDI QIDQ1760119

Dingwen Deng, Cheng-Jian Zhang

Publication date: 12 November 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.07.004

zbMATH Keywords

convergenceADI methodhigher-order compact difference schemenonlinear telegraphic equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)

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Cites Work

• Tension spline approach for the numerical solution of nonlinear Klein-Gordon equation
• Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
• Maximum norm error estimates of efficient difference schemes for second-order wave equations
• High order compact alternating direction implicit method for the generalized sine-Gordon equation
• Solution of non-linear Klein-Gordon equation with a quadratic non-linear term by Adomian decomposition method
• Upwind compact finite difference scheme for time-accurate solution of the incompressible Navier-Stokes equations
• Numerical methods for viscous and nonviscous wave equations
• Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation
• A spline collocation approach for the numerical solution of a generalized nonlinear Klein-Gordon equation
• Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms
• Fourth-order compact solution of the nonlinear Klein-Gordon equation
• Compact finite difference schemes with spectral-like resolution
• Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme
• Numerical solutions of a damped sine-Gordon equation in two space variables
• The solution of the two-dimensional sine-Gordon equation using the method of lines
• A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems
• Numerical solution of the nonlinear Klein-Gordon equation
• Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
• Numerical Solution to the Sine-Gordon Equation Defined on the Whole Real Axis
• Fourth‐order compact scheme for the one‐dimensional sine‐Gordon equation
• An Unconditionally Stable ADI Method for the Linear Hyperbolic Equation in Three Space Dimensions
• A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients
• A new alternating‐direction finite element method for hyperbolic equation
• A new high-order algorithm for a class of nonlinear evolution equation
• High order implicit collocation method for the solution of two‐dimensional linear hyperbolic equation
• New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations

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