The Method of Successive Integration: a General Technique for Recasting Kinetic Equations in a Readily Soluble Form Which Is Linear in the Coefficients and Sufficiently Rapid for Real Time Instrumental Use.

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Abstract
Most simple chemical kinetic models which involve first or higher order processes may be transformed to be linear in their coefficients by one or more exact integrations of the function with respect to time. Thus, a function which is non-linear in time is converted into a function which is linear in two or more dimensions, and is readily solved using simple numerical integration and linear algebra. The simple cases, involving one first or second order step, yield rates which are simple functions of the determined coefficients and may be used directly. More complicated models, involving multiple exponential factors yielding rates and amplitudes which are complex functions of the determined coefficients, yield better fits after iterative improvement of the original unintegrated function. In all cases, the rates and amplitudes obtained do not differ significantly from those using the classic Levenberg-Marquardt algorithm. The method of successive integration is very fast (three to five times faster than Levenberg-Marquardt) and requires neither initial guesses nor approximation of rates and amplitudes.