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IBM Journal of Research and Development  
Volume 19, Number 4, Page 384 (1975)
Nontopical Issue
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Interpolation with Discontinuous Functions: Application to Calculation of Shocks

by W. L. Miranker, A. Morreeuw
An interpolation procedure, which uses a step function plus a polynomial correction, is devised and studied for application to the numerical solution of problems having discontinuous solutions. We apply the interpolation procedure to the calculation of shock waves produced by a single convex conservation law. The resulting algorithm does not have the usual undesirable numerical features associated with shock-wave calculations. The stability and convergence of the algorithm is also demonstrated.
Related Subjects: Computational methods; Mathematics