DEQ
Analytical IVP ODEs 2 integration
Analytical and solve_ivp, known solution.
2026.Jun.03 21:58:39
t0, tF, t* N = 2 Times: from, to (integration) and report.
Parameters Problem parameters (e.g., rates).
IV, initial F values (N values) Values at initial t (IVs).
Target F values (N values) Target function values at t*.
Analytical or numerical   Method of integration for optimization.
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. Reports the function values at t*. Compares with known function.

(Not shown: the 2 embedded ODEs) With the default data, the expected IVs are: (7.6214, 4.3786).

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

Draws a plot of the integrated and known functions.

Computation structure: a PHP file (this page: 'P.analyt.php') calls (via 'action=...') an intermediate PHP file ('Analyt.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 two; analytical; solve_ivp; Python; gnuplot.

References: Plate: analytODE2

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

• Gnuplot dashtype • HTML Color Codes • Python f-string • (Python) unicode characters • Python f-string: A Complete Guide

• 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.

• 1774-04-21: Biot, Jean Baptiste (†1862-02-03, 87 yrs.).

 
 
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Created: 2026-04-21 — Last modified: 2026-04-30