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A detailed derivation and analysis of an implicit factored scheme is given. A one dimensional shock tube problem is solved numerically using the factored scheme. The results and exact solution are presented for this problem. An analysis of the features of the method is made and the limitations of this implicit factored scheme for more general applications to shock waves in solids are discussed. An alternative approach appears to have wider applicability than the method studied here. Keywords: Shock waves; Finite difference algorithms; Simulation, Australia.

This is the first of two related Faraday projects. It is about Faraday and deals more with biographical references to Faraday, outlining the important junctures in his life. The second, <a href="https://librivox.org/on-the-various-forces-of-nature-by-michael-faraday">On the Various Forces of Nature</a>, consists of lectures by Faraday covering a non-mathematical survey of the fundamental forces of nature and some relationships among them. <br><br> Future projects will feature the 19th century scientists upon whose shoulders Einstein stood while developing his Theory of Relativity, including Humboldt, Lorentz, Michelson, Morley, Curie and Eddington. Summary by William A Jones