Is it possible to use the 4th Runge-Kutta method to solve 2nd order ODE (without converting or converting) it into 2 first order state equations? for example: y"+7y'+10y=20,y(0)=5,y'(0)=3 plese write code. Tnx alot.
MATLAB: Is it possible to use the Runge-Kutta method to solve 2nd order ODE (without converting or converting) it into 2 first order state equations
ruge kutta 4th
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Writing a new answer so that I can use markup (MathWorks, please fix this!!). You need a couple of things - first, the time values
t = 0:h:100You can now work out how many steps you need:
n = numel(t)Now, we need an array in which to store your results: each column should correspond to a value from your t vector
x = zeros(2, n)We know the initial condition, so we'll pop that in
x(:, 1) = [0; 0]Now we need a loop to store the subsequent x values. The basic structure will look like this
for i = 2:n % We've already filled in the first column
k1 = h*f(x(:, i-1)); k2 = ... k3 = ... k4 = ... % Now define the new x vector based on k1, ... , k4
x(:, i) = x(:, i-1) + ...end% Plot your results
plot(t, x)And that should pretty much be all you need
Here is the mistake
SOlution
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