Tenth MSU Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 23 (2016), pp. 139-154.

A generalization of prefactored compact schemes for advection equations

Adrian Sescu

A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational load associated with inverting multi-diagonal matrices is avoided, while the order of accuracy is preserved. The prefactorization can be applied to any centered compact difference scheme with arbitrary order of accuracy (results for compact schemes of up to sixteenth order of accuracy are included in the study). One notable restriction is that the proposed schemes can be applied in a predictor-corrector type marching scheme framework. Two test cases, associated with linear and nonlinear advection equations, respectively, are included to show the preservation of the order of accuracy and the increase of the computational efficiency of the prefactored compact schemes.

Published March 21, 2016.
Math Subject Classifications: 65M06, 65M15, 35L02.
Key Words: Compact difference scheme; Transport equation; discretization error.

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Adrian Sescu
Mississippi State University
Mississippi State, MS 39762, USA
phone 1-662-325-7484, fax 1-662-325-7730
email: sescu@ae.msstate.edu

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