|
ODEs Two,
reverse Reverses to find
initial values in ODE's. |
|
|
| t0,
tF, t* |
|
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*. |
| Integration method |
|
Method of integration. |
| Tolerances |
|
Relative and absolute tolerances for integration. |
| Minimization method |
|
Python 'optimization minimization' method. |
| y-axis |
(a: automatic) |
Axis min and max bounds. |
| Points |
|
N. of plot points (0, auto) |
| Show values |
|
Show graph coordinates. |
Integrates the ODEs to
tF. Reports the function values
at t*.
The embedded ODE's are:
x' = -x + k1 x y,
y' = -y + k2 x²,
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.ode2.php') calls (via
'action=...') an intermediate PHP file ('Ode2.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; reverse kinetics;
Python; gnuplot. |
|
References: |
Plate: reverseODEsTwo |
• 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.
• 1926-05-01: Lax, Peter David
(†2025-05-16, 99 yrs.). |
