runge-kutta method funciton in matlab

To implement the Runge-Kutta method in MATLAB, you can define a function that computes the derivative of your function and pass that function to the built-in ode45 function which will use Runge-Kutta to solve the differential equation.

Here is an example function that implements the Runge-Kutta method:

main.m
function [t, y] = runge_kutta(f, tspan, y0, h)
% f: Function handle to the derivative function
% tspan: [t0, tf] - initial and final time values
% y0: Initial value of the function
% h: Step size

t = tspan(1):h:tspan(2);
y = zeros(size(t));
y(1) = y0;

for i = 1:length(t)-1
    k1 = h*f(t(i), y(i));
    k2 = h*f(t(i) + h/2, y(i) + k1/2);
    k3 = h*f(t(i) + h/2, y(i) + k2/2);
    k4 = h*f(t(i+1), y(i) + k3);
    y(i+1) = y(i) + 1/6*(k1 + 2*k2 + 2*k3 + k4);
end

end
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Assuming you have already defined a derivative function f(t, y), you can call this function as follows:

main.m
>> [t, y] = runge_kutta(@f, [0, 10], 1, 0.1);
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This will solve the differential equation defined by f with initial condition y(0) = 1 and final time t = 10 using a step size of h = 0.1. The resulting t and y vectors will contain the time and function values at each step.