Abstract
Data redundancy methods evaluate the output of a program on a given input by examining the outputs produced by the same program on additional inputs. This papers explores the use of data redundancy to detect and/or tolerate failures in differential equation solvers. Our first goal is to show that data redundancy techniques are applicable to a wide class of differential equations. Our second task is to identify circumstances in which an independence model of the sort used in program checking can be exploited to build highly reliable solvers from moderately reliable components. We conclude with illustrative examples of applying various data redundancy techniques to a standard differential equation solver. The method has potential for critical systems in which the application’s control laws are specified as sets of differential equations.
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Ammann, P., Lukes, D.L. & Knight, J.C. Applying data redundancy to differential equation solvers. Annals of Software Engineering 4, 65–77 (1997). https://doi.org/10.1023/A:1018958526071
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DOI: https://doi.org/10.1023/A:1018958526071