solve an ode with three methods in the same script

Hi all,

I have a differential equation and I want to solve it using Runge Kuta, Midpoint method and euler.

So far I have created a function which includes the differential equation, called differential.m

I have created three script which correspond to each method. Those scripts call the differential function.

Names of the scripts are:

euler_method.m

runge_kuta.m

midpoint_method.m

I want to create a function which includes all those scripts and in the work space the results from each method appear.

SO far I wrote this

function mainfunction=mainfunction(t,x)

runge_kuta

euler_method

Midpoint_method

end

But in the workspace nothing appears and in the command window only the results from the midpoint method appear

Answer 1

[Jan]

Each function has its own workspace. The results of the called scripts are stored in the workspace of the function mainfunctionm but not in the base workspace, which is active in the command window.

Your code creates an error message, if it is called with an output:

function mainfunction=mainfunction(t,x)
...
end

Inside the function, the variabke "mainfunction" is not created, so it cannot be replied.

A solution is to convert the code for the integrations from scripts to functions:

function mainfunction(fcn, t, x0)
x_runge = runge_kutta(fcn, t, x0);
x_euler = euler_method(fcn, t, x0);
x_mid   = Midpoint_method(fcn, t, x0);

% Now add some code here for plotting the results
end

Call this function as:

mainfunction(@differential, t, x0)

In the integrator functions replace differential() by fcn().

[Ilias Minas]

The script for runge kutta for example is the followng

h=1; % step size

t = 0:h:11; % Calculates upto x(3)

x = zeros(1,length(t));

%x(1) = [-0.5;0.3;0.2];

x(1) = 1; % redo with other choices here.

% initial condition

% change the function as x_rgou desire

for i=1:(length(t)-1) % calculation loop

k_1 = differential(t(i),x(i));

k_2 = differential(t(i)+0.5*h,x(i)+0.5*h*k_1);

k_3 = differential((t(i)+0.5*h),(x(i)+0.5*h*k_2));

k_4 = differential((t(i)+h),(x(i)+k_3*h));

x(i+1) = x(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; % main equation

end

in which 'differential' is the equation.

Do I need to convert this or create a function in the beggining?

I tried the way that you proposed but the following error appears

mainfunction

Not enough input arguments.

Error in mainfunction (line 2)

x_runge = runge_kuta(differential, t, x)

[Jan]

"mainfunction - Not enough input arguments" - how did you start the function? With the suggested:

mainfunction(@differential, t, x0)

?

What are the inputs t and x? The time steps and the initial value? Then this is a Runge-Kutta function for the integration based on your script:

function x = runge_kutta(fcn, t, x0)
h = t(2) - t(1);
x = zeros(1, length(t)); 
x(1) = x0;
for i = 1:numel(t) - 1
    k_1 = fcn(t(i),           x(i));
    k_2 = fcn(t(i) + 0.5 * h, x(i) + 0.5 * h * k_1);
    k_3 = fcn(t(i) + 0.5 * h, x(i) + 0.5 * h * k_2));
    k_4 = fcn(t(i) + h,       x(i) + k_3 * h));
    x(i+1) = x(i) + (h/6) * (k_1 + 2 * k_2 + 2 * k_3 + k_4);
end
end

Now the function is general and you can use it for all functions, time points and initial values. Convert the other scripts accordingly.