An implicit finite difference approximation to the one-dimensional transport equation

Frank G. Polanco, Robert L. May


The properties of an implicit three-level finite difference scheme are investigated. The modified equivalent partial differential equation is used to determine the speed and amplitude characteristics of the scheme, and these are used to determine the optimal value of the weighting between a central difference and an upwind biased difference. Results of numerical experiments that confirm that the predicted value of the weight does minimise the error are presented.

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.