Python:Ordinary Differential Equations/Templates

The codes below present templates for creating the function file responsible for computing values of the first derivatives of all the variables and the script whose job is to solve a system of initial value problems based on ordinary differential equations. This program calls the StatePlotter program, available at the bottom.

Code

#%% Imports
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp

#%% Define independent function and derivative function
def x(t):
    return # Independent function here

def f(t, y, c):
'''
Template for calculating first derivatives of state variables
t is time
y is the state vector
c contains any required constants
dydt must be a list or an array
'''
    dydt = # list or array of first derivatives here
    return dydt
    
#%% Define time spans, initial value, and extra constants
tspan = 
yinit = #must be a list or an array
c = 

#%% Solve differential equation
sol = solve_ivp(f, [tspan[0], tspan[-1]], yinit, t_eval=tspan)

#%% Determine if states should be plotted
plot_states = True;

#%% Plot independent and dependent variable

State Plotter

The StatePlotter.m code will accept a vector of times and a matrix of states (which should have each state in a column). It will determine how many states there are based on the number of columns, break the figure window up into the appropriate number of subplots, and graph each state.

function StatePlotter(Time, States)

StateCount = size(States, 2);

NumCols = ceil(sqrt(StateCount));
NumRows = ceil(StateCount / NumCols);
clf;
for PlotNumber = 1:StateCount
        subplot(NumRows, NumCols, PlotNumber);
        plot(Time, States(:,PlotNumber), 'ko:');
        xlabel('Time');
        ylabel(sprintf('y_{%0.0f}(t)', PlotNumber))
        title(sprintf('y_{%0.0f}(t) vs. Time', PlotNumber));
end

Questions

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