why do i receive this error

x=0.1;
x= 0:0.1:1;
yic =[1  -2] ' ;
for i=1:(length(x)-1)
    K11 = fn (x, yic);
    K21 = fn (x , yic);
    K12 = fn ((x + h) , (yic + (h*K11)) , (yic + (h*K21)));
    K22 = fn ((x + h),(yic + h*K11) , (yic + h*K21));
    y1 = ( yic + 0.5*h*(K11  + K12 ));
    y2 = ( yic + 0.5*h*(K12  + K22)); 
end


function f = fn( x , yic )
dy = yic(2);
dy2 = 2*yic(1)-yic(2);
end

when i run the code this error appear :

''

Output argument "f" (and maybe others) not assigned during call to "HW2>fn".

Error in HW2 (line 22)

K11 = fn (x, yic);

''

Answer 1

[Sergey Kasyanov]

Hello!

You don't define f in fn function.

Are you want to return f = [fy, fy2]? In that case:

function f = fn( x , yic )
dy = yic(2);
dy2 = 2*yic(1)-yic(2);
f = [dy, dy2];
end

Also you have an error in another lines. Maybe you should to correct it in that way:

 K12 = fn ((x + h) , [(yic + (h*K11)) , (yic + (h*K21))] );
 K22 = fn ((x + h),  [(yic + h*K11) , (yic + h*K21)] );

[Mohammad Adeeb]

i want the code to take those values of [dy , dy2] and then get thme in the for loop

[Sergey Kasyanov]

What are you need to do in global?

[Mohammad Adeeb]

im trying to write a code to solve 2nd order ode by using reduction of order and runge-kutta 4th order method

[Mohammad Adeeb]

the code run , but the value of y is only matrix 2*2 , and its should be 11*2

[Sergey Kasyanov]

Can you write the equation?

[Mohammad Adeeb]

d2y/dx2 +dy/dx-2y=0

but i should use my own function not a built in one

[Mohammad Adeeb]

i did the following changes to my code

clear all;
close all;
clc;

h=0.1;          %step size
x=0:h:1; %the X domain range
yic = [1  -2]';         %intial condition

t=exp(-2*x);


for i=1:(length(x)-1)
    K11(i) = fn (x(i), yic(i));
    K21(i) = fn (x(i) , yic(i));
     K12(i) = fn ((x(i) + h) , [(yic(i) + (h*K11(i))) , (yic(i) + (h*K21(i)))] );
     K22(i) = fn ((x(i) + h),  [(yic(i) + h*K11(i)) , (yic(i) + h*K21(i))] );
    y1(i+1) = ( yic(i) + 0.5*h*(K11(i)  + K12(i) ));
    y2(i+1) = ( yic(i) + 0.5*h*(K12(i)  + K22(i))); 
end

plot(x,y1,'k*')
hold on;
plot(x,y_exact,'r.-')
xlabel('X axis')
ylabel('Y axis')
legend('Y_e_x_a_c_t','Y_a_p_p')

function f = fn( x , yic )
dy = yic(2);
dy2 = 2*yic(1)-yic(2);
end

.

but i recive the following error :

Index exceeds the number of array elements (1).

Error in HW2>fn (line 41)

dy = yic(2);

Error in HW2 (line 25)

K11(i) = fn (x(i), yic(i));

[Sergey Kasyanov]

h = 0.1;
x = 0:h:1;
y = [[1;-2],zeros(2, length(x)-1)];

for i = 1:length(x)-1
    K1 = f(x(i), y(:, i));
    K2 = f(x(i) + h/2, y(:, i) + h*K1/2);
    K3 = f(x(i) + h/2, y(:, i) + h*K2/2);
    K4 = f(x(i) + h,   y(:, i) + h*K3);
    y(:, i+1) = y(:, i) + h/6*(K1 + 2*K2 + 2*K3 + K4);
end

function dy = f(x, y)
    dy = [0,  1
          2, -1] * y;
end


plot(x, y(1,:), 'k*');

[Mohammad Adeeb]

thank u so much ; but i have qustion why do you use dy as matrix and multiply it by y

[Walter Roberson]

Writing it that way is just a more compact way of writing it.

[Sergey Kasyanov]

It is more readable.