Abstract
Our earlier paper incorporated linear basis functions for the representation of the distribution of the primary variable (velocity) into a model of the Green element method (GEM) for the solution of Burgers' equation. GEM is an element-by-element numerical procedure of implementing the singular boundary integral theory which yields a banded coefficient matrix that is easier to decompose, thereby enhancing computational efficiency. The performance of that earlier model depended partly on how well the velocity was represented. For shock propagation problems in which large gradients of the velocity are encountered, the use of linear interpolation functions may be inadequate. Here, we incorporate the cubic Hermitian interpolation functions into that same model, and demonstrate that the accuracy of the numerical solution of Burgers' equation is enhanced, but at a higher computing cost. Copyright © 1999 John Wiley & Sons, Ltd.
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