DEQ
IVP ODEs one
Reverses to find initial values in ODE's. UNDER CONSTRUCTION
2026.Jun.03 21:58:39
tF, t*   (tR := min(tf, tR)) Times: final integration (from 0) and report.
Initial F values Values at t = 0 (IVs).
Target F values Target function values at t*.
Parameters Problem parameters (such as rates).
Integration method        Method of integration.
Tolerances Relative and absolute tolerances for integration.
Minimization method Python 'optimization minimization' method.
Points N. of plot points (0, auto)
Show values Show graph coordinates.

Integrates the ODEs from time 0 to tF. Reports the function values at t*.

The embedded ODE's are:  x' = -a²b sin(2bt) ⁄ [1 + a²cos²(bx)]², with given initial values.

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

Draws a plot of the integrated functions.

Computation structure: a PHP file (this page: 'P.ivp.php') calls (via 'action=...') an intermediate PHP file ('Ivp.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) web page.

Keywords: ODEs one; reverse kinetics; Python; gnuplot.

References: Plate: reverseODEsOne

• Python minimize [in Optimization and root finding (scipy.optimize)].

• Gnuplot dashtype • HTML Color Codes • Python f-string • (Python) unicode characters

• 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.).

 
 
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Created: 2026-04-17 — Last modified: 2026-04-17