Improvements in a single-step integration algorithm

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Abstract
THis paper describes and illustrates extensions and iimprovements to a particularly efficient numerical integration method which was first presented in the July 1974 issue of Simulation.5 The algorithm is a single-step A-stabZe implicit method. The recent improvements provide better control over error in both integration and roundoff and greater computa tional efficiency than current methods for both linear and nonlinear systems. The results of apply ing the new algorithm to seven benchmark problems are reported and are compared with results obtained in solving the same problems by Gear's method.