2015-Knott, G. D. and D. Kerner - Numerical to Closed Form Solution - Derivation
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Knott, G. D. and D. Kerner. 2015. Derivatives. Civilized Software, Inc. Publishers of MLAB: www.civilized.com.
This is a very nice technical paper on moving from numerical solutions to closed form analytic solutions as evidence of convergence of numerical efforts and is offered by the developers of MLAB, an advanced mathematical and statistical modeling system, is an ideal tool for mathematical and statistical exploration, and for solving simulation and modeling problems such as chemical kinetics, pharmacological compartmental models, multiple site ligand binding, neurophysiological modeling, and ultracentrifuge models, to name just a few. MLAB is especially designed to handle differential equation models.
We quote from the paper, "What we have done above is solve the first-order linear ordinary differential equation A’(t) = r A(t). We were able to convert our differential equation and its initial condition into a sequence of linear equations and collapse these linear equations into a single equation yielding the solution. In more general situations, we may have `uncollapsable' equations, but we can still proceed numerically; our sequence of equations then form an algorithm."
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