DEQ
Reverse kinetics
Reverses kinetics to find initial values in ODE's. UNDER CONSTRUCTION
2026.Apr.10 18:13:37
tf, tR   (tR := min(tf, tR)) Final integration time (from 0) and report.
Target F values Target function values at tR.
Initial values Values at t = 0 (IVs).
Rates Rates (α, β, γ, ν).
Integration method        Method of integration.
Computation mode     Mode, and termination tolerance.
Minimization method Python 'optimization minimization' method.
Points N. of points in plot
Show values Show graph coordinates.

Integrates the ODEs from time 0 to tf. Reports the function values at tR.

The embedded ODE's are in Fig., with (x, y, y)0 the given initial values.

This applies, from Python: for integration, 'scipy.integrate' 'odeint'; and, for optimization, 'minimize'.

Advantage is taken from: PHP, for the web page; Python for the numerical segment; and 'gnuplot', for plotting.

Draws a plot of the data.

ODEs

Computation structure — A PHP file (this page: 'P.reverse.php') calls (via 'action=...') an intermediate PHP file ('Reverse.php'), which (through $_POST) sends the problem data as command line arguments to a Python script. This last does the computing, and makes 'system' call(s) to 'gnuplot', for the final (temporary) webpage.

Files involved: P.reverse.php (this one), Reverse.php, reverse.py.

Keywords: reverse kinetics; PHP; Python; gnuplot.

References: Plate: reverseKinetics

#• From "Parameter Estimation for a Chemical Reaction" (Maplesoft) Reported (nonnegative): k = (0.0632294, 0.0186954, 0.0144413, 0.)

• Python minimize [in Optimization and root finding (scipy.optimize)], accessed 12-Dec-2023.

• Gnuplot dashtype • HTML Color Codes • Python f-string

• CISTI'2027, 22.ª Conferência Ibérica de Sistemas e Tecnologias de Informaçaão (22.nd Iberian Conference on Information Systems and Technologies), #... (Portugal), #25–28 June 2027.

• 1902-04-04: Hopf, Eberhard Frederich Ferdinand (†1983-07-24, 81 yrs.).

 
 
Valid HTML 5! IST http://web.ist.utl.pt/~ist11038/compute/reverse/P.reverse.php
Created: 2026-04-04 — Last modified: 2026-04-06