Nonlinear ODEs

Nonlinear ODEs integration

Integration of nonlinear differential equations UNDER CONSTRUCTION

2025.Feb.21 18:13:54

t_i, t_f

Initial and final times.

Parameters (a, b, c)

Parameters in ODE.

Initial values (y_i, y'_i)

IVP: function and derivative.

Method

RK45 RK23 DOP853 Radau BDF LSODA

Method of integration.

Points

N. of plot points.

Show values

Show graph coordinates.

Integrates a 2.nd order nonlinear ODE, transformed into a system of ODEs, with given parameters and initial values of y_i and y'_i.

The objective would be to obtain y(3) = 14⁄3 ≈ 14.3, by manipulating y'_i.

Files involved: P-nonlinear.php (this one), Nonlinear.php, nonlinear.py.

Integration is by Python 'scipy' module solver solve_ivp, with the selected method of numerical integration.

Shows the graphical results of the solved ODEs.

References:

Plate: Nonlinear

• (Wikipedia) PHP (from Personal Home Page)

• Remani, C., 2013, "Numerical Methods for Solving Systems of Nonlinear Equations", Lakehead U.

• CISTI'2026, 21.ª Conferencia Ibérica de Sistemas y Tecnologías de Información (21.st Iberian Conference on Information Systems and Technologies), Sevilla (Spain), 15–18 June 2026, to be confirmed.

• 1902-01-24: Morgenstern, Oskar (†1977-07-26, 75 yrs.).

http://web.ist.utl.pt/~mcasquilho/compute/CISTI_2025/nonlinear/P-nonlinear.php
Created: 2025-01-24 — Last modified: 2025-01-24