Some general implicit processes for the numerical solution of differential equations

1963/04/01 by H.H. Rosenbrock, H. H. Rosenbrock · 6 citations
Mathematics · Computer Science · Engineering · #Numerical methods for differential equations #Modeling and Simulation Systems #Electromagnetic Simulation and Numerical Methods

paper · pdf · doi:10.1093/comjnl/5.4.329

Abstract

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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