Non-linear evolution using optimal fourth-order strong-stability-preserving Runge-Kutta methods

DOI10.1016/S0378-4754(02)00179-9zbMath1015.65031OpenAlexW2005665126MaRDI QIDQ1869177

Publication date: 9 April 2003

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-4754(02)00179-9

zbMATH Keywords

algorithms conservation laws numerical examples method of lines evolution Runge-Kutta schemes discontinuous or shock-like solutions strong-stability-preserving time discretization methods total-variation-diminishing methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) First-order nonlinear hyperbolic equations (35L60) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical investigation of stability of solutions to ordinary differential equations (65L07)

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Cites Work