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Two new packages are available for the numerical solution of the initial value problem for stiff and nonstiff systems of ordinary differential equations (ODE's). LSODE solves explicitly given ODE systems, while LSODI solves systems given in linearly implicit form, including differential-algebraic systems. Both are based on older packages that have proved highly popular, but both reflect a wide variety of improvements in the design of the user interface, algorithms, and program structure.
A.C. Hindmarsh (Mon,) studied this question.