ordinary differential equations in matlab

To solve ordinary differential equations (ODEs) in MATLAB, you can use the built-in function ode45. ode45 is a versatile function that can handle a wide range of ODEs.

Here is the general syntax for using ode45 to solve an ODE:

main.m
[t, y] = ode45(@odefun, tspan, y0)
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• odefun is a function handle that defines the ODE. It should take two inputs: the current time t and the current state y, and return the derivative of y with respect to t at that point.

• tspan is a vector specifying the time span of integration. It can be a two-element vector [t0, tf] for integrating from t0 to tf, or a longer vector [t0, t1, t2, ..., tf] for integrating over multiple time intervals.

• y0 is a vector specifying the initial condition of the ODE.

• The output t is a column vector containing the time points at which the solution is calculated.

• The output y is a matrix where each column represents the solution of the ODE at the corresponding time point in t.

Here is an example to demonstrate the usage of ode45:

main.m
% Define the ODE function
function dydt = odefun(t, y)
    dydt = -2*y;
end

% Define the time span and initial condition
tspan = [0 10];
y0 = 1;

% Solve the ODE using ode45
[t, y] = ode45(@odefun, tspan, y0);

% Plot the solution
plot(t, y)
xlabel('t')
ylabel('y')
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This code solves the ODE dy/dt = -2*y from t = 0 to t = 10 with the initial condition y(0) = 1. The solution is then plotted.

Note: Make sure to define your ODE function properly according to the specific ODE you want to solve.