A universal solver for hyperbolic equations by cubic-polynomial interpolation. I: One-dimensional solver
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Publication:1366042
DOI10.1016/0010-4655(91)90071-RzbMath0991.65521MaRDI QIDQ1366042
Publication date: 2 September 2002
Published in: Computer Physics Communications (Search for Journal in Brave)
Korteweg-de Vries equationhyperbolic equationscubic polynomialfinite-difference formone-dimensional shock-tube problem
Shocks and singularities for hyperbolic equations (35L67) KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05) Numerical interpolation (65D05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial value problems for first-order hyperbolic systems (35L45)
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Cites Work
- The cubic-interpolated pseudo particle (CIP) method: Application to nonlinear and multi-dimensional hyperbolic equations
- The piecewise parabolic method (PPM) for gas-dynamical simulations
- Second-order fluid particle scheme
- Numerical calculations of discontinuities by shape preserving splines
- Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic- type equations
- The representation of shock-like solutions in an Eulerian mesh
- A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
- A universal solver for hyperbolic equations by cubic-polynomial interpolation. II: Two- and three-dimensional solvers
- Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
- On a Class of High Resolution Total-Variation-Stable Finite-Difference Schemes
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