runge-kutta-fehlberg matlab

Runge-Kutta-Fehlberg (RKF45) is a numerical method used for solving differential equations. It is a higher order method that provides an accurate solution with a relatively small number of function evaluations.

Matlab has a built-in function called "ode45" that implements the RKF45 method. It takes as input the differential equation to be solved, the initial conditions, and the integration interval. The output is a vector of solution values at specified time points.

Here is an example code that uses ode45 to solve the differential equation y' = y^2 - t^2 with initial condition y(0) = 1:

function rkf45_demo
    % Define the differential equation
    f = @(t,y) y^2 - t^2;
    
    % Define the initial conditions and integration interval
    tspan = [0, 1];
    y0 = 1;
    
    % Call ode45 to solve the differential equation
    [t, y] = ode45(f, tspan, y0);
    
    % Plot the solution
    plot(t, y);
    xlabel('t');
    ylabel('y');
    title('Solution of y'' = y^2 - t^2');
end

Note that the RKF45 method is just one of many numerical methods available in Matlab. Depending on the specific differential equation being solved, a different method may be more appropriate.