I'm trying to write a matlab function to solve RK4 and store it in my computer to be called when needed.

Below is my attempt at the function but when it is run there are issues. could someone correct it and post their version?

function [x,y] = Rk4(dy_dx,x_1,y_1,x_end,h_step)

%dy_dx = differential function

%x_1 = first x value

%y_1 = first y value

%x_end = final x value

%h_step = step size

%Initialize

syms x y(x) u;

dy_dx(x, u) = subs(dy_dx, y(x), u);

dy_dx = matlabFunction(dy_dx); % lets matlab interpret the value as a number

%Initialize Storage

x_all = [x_1:h_step:x_end];

y_store = zeros(length(x_all));

y_store(1) = y_1;- %makes running this code easier on the computer

%Loop -> Summation

for i = 1:length(x_all)-1

k_1 = dy_dx(x_all(i), y_store(i));

k_2 = dy_dx(x_all(i) + 0.5*h_step, y_store(i) + 0.5*h_step*k_1);

k_3 = dy_dx(x_all(i) + 0.5*h_step, y_store(i) + 0.5*h_step*k_2);

k_4 = dy_dx(x_all(i) + h_step, y_store(i) + h_step*k_3);

y_store(i+1) = y_store(i) + h_step*(k_1 + 2*k_2 + 2*k_3 + k_4)/6;

end

%Results

y_store(length(y_store))

plot(x_all, y_store);

end

[John D'Errico]

Don't just say there are some issues. That forces someone to spend the time to run it and test it fully, and even then we might not know what you think are the issues. What do YOU think is a problem? If you get an error, then show the COMPLETE error. Everything in red.

Answer 1

[Torsten]

If you call RK4 correctly, it will work.

syms y(x) dy_dx(x)
dy_dx(x) = x + y(x);
x_1 = 0;
y_1 = 1;
x_end = 1;
h_step = 0.01;
[x,y] = Rk4(dy_dx,x_1,y_1,x_end,h_step);

fun = @(x,y) x+y;
[X,Y] = ode45(fun,x_1:h_step:x_end,y_1);

plot(X,Y-y)
grid on

function [x_all,y_store] = Rk4(dy_dx,x_1,y_1,x_end,h_step)

%dy_dx = differential function
%x_1 = first x value
%y_1 = first y value 
%x_end = final x value 
%h_step = step size

%Initialize
syms x y(x) u

dy_dx(x, u) = subs(dy_dx, y(x), u);
dy_dx = matlabFunction(dy_dx); % lets matlab interpret the value as a number 

%Initialize Storage
x_all = [x_1:h_step:x_end];
y_store = zeros(length(x_all),1);
y_store(1) = y_1; %makes running this code easier on the computer


%Loop -> Summation
for i = 1:length(x_all)-1
    k_1 = dy_dx(x_all(i), y_store(i));  
    k_2 = dy_dx(x_all(i) + 0.5*h_step, y_store(i) + 0.5*h_step*k_1);
    k_3 = dy_dx(x_all(i) + 0.5*h_step, y_store(i) + 0.5*h_step*k_2);
    k_4 = dy_dx(x_all(i) + h_step, y_store(i) + h_step*k_3);
    y_store(i+1) = y_store(i) + h_step*(k_1 + 2*k_2 + 2*k_3 + k_4)/6;
end

end