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An explicit finite difference scheme based on the modified method of characteristics for solving convection‐diffusion problems in one space dimension
Author(s) -
Thomaidis George,
Zygourakis Kyriacos,
Wheeler Mary F.
Publication year - 1988
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690040203
Subject(s) - mathematics , convergence (economics) , dimension (graph theory) , overshoot (microwave communication) , convection–diffusion equation , scheme (mathematics) , space (punctuation) , stability (learning theory) , diffusion , convection , mathematical optimization , mathematical analysis , computer science , mechanics , physics , machine learning , pure mathematics , economics , thermodynamics , economic growth , operating system , telecommunications
Finite differences are combined with the modified method of characteristics to develop an explicit scheme for solving convection‐dominated convection‐diffusion problems in one spatial dimension. Error analysis shows that the new algorithm is stable under a mild stability criterion. Problems with known analytical solutions are used to test the algorithm and demonstrate its convergence. Numerical solutions are free of numerical dispersion, undershoot and overshoot. The algorithm is easy to implement and requires small computational times for the test problems considered.