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Higher order accuracy finite‐difference schemes for hyperbolic conservation laws
Author(s) -
Reddy A. Sivasankara
Publication year - 1982
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620180706
Subject(s) - conservation law , mathematics , hyperbolic partial differential equation , order (exchange) , finite difference , partial differential equation , stability (learning theory) , scheme (mathematics) , ftcs scheme , finite difference method , space (punctuation) , order of accuracy , finite difference coefficient , mathematical analysis , differential equation , finite element method , method of characteristics , computer science , ordinary differential equation , mixed finite element method , engineering , differential algebraic equation , finance , machine learning , economics , operating system , structural engineering
An explicit algorithm which gives stable finite‐difference schemes, of order of accuracy greater than two, for solving a quasi‐linear hyperbolic system of partial differential equations in several space dimensions is presented. Third and fourth order accuracy schemes are derived using this algorithm. The fourth order scheme needs fewer flux evaluations than the scheme given by Abarbanel and Gottlieb. 1 Numerical results obtained show that these schemes have the expected accuracy and stability.