% IAP 2006 Introduction to MATLAB
% Ordinary Differential Equations (ODE)

% EXAMPLE 3 Current and Voltage through a Parallel RC Circuit
% Based on the MATLAB Mastery Tutorial at:
% https://web.mit.edu/tm/matlab_mastery_I/setup/Start.htm
% Find a numerical solution for the current I and voltage drop V for a
% capacitor with initial charge q0 draining through a resistor R.

% A. Solve ODE based on Ohm's law for RC circuit
% ODE for the capacitor's rate of discharge is:
% R * (dq/dt) + q / C = 0
% where R is the resistance of the resistor in Ohms,
% and C is the capacitance of the capacitor in farads.
% The equation can be re-written as: dq/dt = -1/(R*C) * q

% A1. Define global variables C and R
% Global variables can be accessed from other files. For example:
global R C
C = 0.002
R = 150

% A2. Define function Dq = ode(t, q)
% Dq is defined in the function M-file called ode.m
% Dq is a variable that stands for dq/dt
% See file ode.m for the definition of Dq before proceeding here

% A3. Define condition at time t=0
% The charge is q0 in coulombs; for example:
q0 = -0.001
% We can call the function ode to compute dt/dq at t=0
Dq0 = ode(0, q0)

% A4. Compute solution of ODE
% Define time interval
tspan = [0 : 0.01 : 1]

% A5. Compute numerical solution using the ode45 function
% ode45 is a built-in function for solving nonstiff diferrential equations.
[t, q] = ode45( @ode, tspan, q0 )
% Note that the function ode is passed to ode45 as a Function Handle @ode.

% A6. Plot the numerical solution
plot(t, q, 'g')
grid on

% A7. Compute the current I over time
% The current is the derivative of the charge q i.e. dq/dt.
% To compute I over time, we pass the vectors t and q to ode:
I = ode(t, q);

% A8. Compute the voltage drop across the resistor over time
V = I*R

% A9. Plot I and V on a semilogarithmic plot
semilogy(t, I, 'r-')
hold on
semilogy(t, V, 'b-')
grid on
hold off
xlabel('Time')
ylabel('Voltage drop V and current I')
legend('V', 'I')
title('RC Circuit')

% A10. See Solving 2nd Order ODE in the MATLAB Mastery Tutorial
% Sellect the Differential Equations module and go to part 2 of it
% https://web.mit.edu/tm/matlab_mastery_I/setup/Start.htm