Exponentially fitted IMEX methods for advection-diffusion problems

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• 作者：Angelamaria Cardone ^{ancardone@unisa.it} ; Raffaele D'Ambrosio ; ^{rdambrosio@unisa.it} ; Beatrice Paternoster ^{beapat@unisa.it}
• 关键词：Advection&ndash ; diffusion problems ; Finite differences ; Exponential fitting ; IMEX methods ; Stability analysis
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：316
• 期：Complete
• 页码：100-108
• 全文大小：1395 K
• 卷排序：316

文摘

The paper is devoted to the numerical solution of advection–diffusion problems of Boussinesq type, by means of adapted numerical methods. The adaptation occurs at two levels: along space, by suitably semidiscretizing the spatial derivatives through finite differences based on exponential fitting; along time integration, through an adapted IMEX method based on exponential fitting itself. Stability analysis is provided and numerical examples showing the effectiveness of the approach, also in comparison with the classical one, are given.