how can I do Iteration in matlab

I have an equation of the form

a(x) + x.da/dx = 2x , x= 1:1:12

f(x) is known and has different values for different x. My question is how can I find values of 'a' in matlab through iteration. Am new to matlab and any help is highly appreciated.

Answer 1

save this function with the name dif_eq

function da=dif_eq(x,a,tim,f)
f1=interp1(tim,f,x)
da=(f1-a)/x;

then call the function:

 t=[0.1:10]; % time vector
 x0=0; % initial condition
 f=rand(1,numel(t)); % your vector f, same length as vector time t
 [X,A]=ode45(@(x,a) dif_eq(x,a,t,f),t,x0);
 plot(X,A)

Many many thanks ...don't have words for your help....this was so troublesome...

Answer 2

save this funnction with the name dif_eq

function da=dif_eq(x,a)
f=sin(x); for example
da=(f-a)/x;

then type in Matlab command

[x,res]=ode45(@dif_eq,[1 12],0)

Thanks Azzizi can you clarify me how can I insert the 'f' value in my command and the second is this equation can solve the differential part of the equation. My equation is a(x) + x.da/dx = f(x),

You said that f is a function of x, then replace in my code, f=sin(x) by your own function

The code I did solves your differential equation

Yes, I did that my actual 'f' is not function actually it is collection of different values. such as 0.4 0.25 0.6.....

Thanks Azziz , I understand your function but 'a' itself isn't known and that's my problem.

Ede, the problem is not a, we are looking for a. I can't use f with different values in the equation. If I find something I will post it, or someone else will do.