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In a recent article in the Communications of the ACM, R. Wengert suggested a technique for machine evaluation of the partial derivatives of a function given in analytical form. In solving nonlinear boundary-value problems using quasilinearization many partial derivatives must be formed analytically and then evaluated numerically. Wengert's method appears very attractive from the programming viewpoint and permits the treatment of large systems of differential equations which might not otherwise be undertaken.

Wengert's numerical method for partial derivatives, orbit determination and quasilinearization