Linear stability analysis and fourth-order approximations at first time level for the two space dimensional mildly quasi-linear hyperbolic equations

DOI10.1002/num.1029zbMath0990.65102OpenAlexW2125704438MaRDI QIDQ2762699

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Publication date: 18 July 2002

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.1029

zbMATH Keywords

numerical resultsPadé approximationoperator splittinglinear stability analysisfinite differencedamped wave equationquasilinear hyperbolic equation

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)

Related Items (11)

Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms ⋮ A New Fast Numerical Method Based on Off-Step Discretization for Two-Dimensional Quasilinear Hyperbolic Partial Differential Equations ⋮ A high-resolution bi-parametric unconditionally stable ADI method for 2D uniform transmission line equation ⋮ Cosine expansion based differential quadrature algorithm for numerical simulation of two dimensional hyperbolic equations with variable coefficients ⋮ A new high-order approximation for the solution of two-space-dimensional quasilinear hyperbolic equations ⋮ A new unconditionally stable method for telegraph equation based on associated Hermite orthogonal functions ⋮ A numerical method for diffusion-convection equation using high-order difference schemes ⋮ Compact difference schemes for solving telegraphic equations with Neumann boundary conditions ⋮ A new unconditionally stable ADI compact scheme for the two-space-dimensional linear hyperbolic equation ⋮ Numerical solution of second-order two-dimensional hyperbolic equation by bi-cubic B-spline collocation method ⋮ New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations

Cites Work

• Analytical, linear stability criteria for the leap-frog, DuFort-Frankel method
• Fourth-order approximations at first time level, linear stability analysis and the numerical solution of multidimensional second-order nonlinear hyperbolic equations in polar coordinates
• Order \(h^ 4\) difference methods for a class of singular two space elliptic boundary value problems
• High order difference schemes for the system of two space second order nonlinear hyperbolic equations with variable coefficients
• Fourth-order approximation for the three space dimensional certain mildly quasi-linear hyperbolic equation
• Alternating Direction Methods for Hyperbolic Differential Equations
• High Accuracy A.D.I. Methods for Hyperbolic Equations with Variable Coefficients

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