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The Computer Journal 1963 5(4):329-330; doi:10.1093/comjnl/5.4.329
© 1963 by British Computer Society
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Some general implicit processes for the numerical solution of differential equations

H. H. Rosenbrock

University Engineering Laboratory, Cambridge, UK

Some general implicit processes are given for the solution of simultaneous first-order differential equations. These processes, which use successive substitution, are implicit analogues of the (explicit) Runge-Kutta processes. They require the solution in each time step of one or more set of simultaneous linear equations, usually of a special and simple form.

Processes of any required order can be devised, and they can be made to have a wide margin of stability when applied to a linear problem.


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