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Characteristic Analysis of Exponential Compact Higher Order Schemes for Convection-Diffusion Equations
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American Journal of Computational Mathematics·Volume 01 (2011)·Pages 39–54·Published 30 June 2011·DOI10.4236/ajcm.2011.12005
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Abstract
This paper looks at the development of a class of Exponential Compact Higher Order (ECHO) schemes and attempts to comprehend their behaviour by introducing different combinations of discrete source function and its derivatives. The characteristic analysis is performed for one-dimensional schemes to understand the efficiency of the scheme and a similar analysis has been introduced for higher dimensional schemes. Finally, the developed schemes are used to solve several example problems and compared the error norms and rates of convergence.
KeywordsExponential SchemeCompact Higher Order SchemeCharacteristicsResolving EfficiencyFinite Difference
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