Matlab Problem: Runge-Kutta Fehlberg

[iwonde]

Homework Statement

I need to write a Matlab program that solves the following:

Use the Runge-Kutta Fehlberg Algorithm with tolerance TOL= 10^(-4) to approximate the solution to the initial-value problem:
y'=(y/t)^2 + y/t, 1<=t<=1.2, y(1)=1, with hmax=0.05 and hmin=0.02.

Homework Equations

The Attempt at a Solution

%This is the source code for the function rkf.
% w denotes the approximation to y
% h=step size
function [w,t,h]=rkf(a,b,w0,TOL,hmax,hmin)
%Step 1
h=hmax; t=a; w=w0; FLAG=1;

%Step 2
while(FLAG==1)

%Step 3
F1 = h*f(t,w);
F2 = h*f(t+h/4 ,w+F1/4);
F3 = h*f(t+3*h/8,w+ 3*F1/32+9*F2/32);
F4 = h*f(t+12*h/13,w+932*F1/2197-7200*F2/2197+7296*F3/2197);
F5 = h*f(t+h,w+(439*F1)/216-(8*F2)+3680*F3/513-(845*F4)/4104);
F6 = h*f(t+h/2,w-8*F1/27+2*F2-(3544*F3)/2565+1859*F4/4104-11*F5/40);


%Step 4
R = abs(F1/360-128*F3/4275-2197*F4/75240 + F5/50 + 2*F6/55)/h;

%Step 5
if (R<=TOL)

%Step 6
t= t+h;
w= w + 25*F1/216 + 1408*F3/2565 + 2197*F4/4104 - F5/5;
end

%Step 8
delta=0.84*(TOL/R)^(1/4);

%Step 9
if delta <= 0.1
h=0.1*h;
elseif delta>=4
h=4*h;
else
h=delta*h;
end

%Step 10
if h>hmax
h=hmax;
end

%Step 11
if t>=b
FLAG=0;
elseif (t+h)>b
h=b-t;
elseif h<hmin
FLAG=0;
fprintf('minimum h exceeded\n');
return;
end
end
end
=====================================
%I've tried compiling the code with:

a=1; b=1.2; TOL=10^(-4); w0=1; hmax=0.05; hmin=0.02;
f= @(t,w) (w/t)^2 + w/t;
[w,t,h]=rkf(a,b,w0,f,TOL,hmax,hmin);
w
t
h


======================================

The above code didn't work. I'm attempting at a code that outputs something like:
i t_i w_i h_i
---------------------------------
1 1.05
2 1.10
3 1.15
4 1.20

I'm not really sure of how to add in the index for t,w, h to obtain a value at every step. Any help would be greatly appreciated. Thanks!

 

[mighty2000]

Hello!

I took a look at your code and noticed a few things that could be causing issues. First, it seems like you are trying to use the Runge-Kutta Fehlberg method to solve the initial value problem, but your function only takes in the initial values and tolerance. You need to also include the function f(t,w) in your inputs.

Next, it seems like you are trying to output a table with the values at each step, but your function is only outputting the final w, t, and h values. You can try creating a loop inside your function that stores the values at each step and then outputs them at the end.

Lastly, I would recommend checking your implementation of the method itself to make sure it is correct. You can try testing it with a simpler problem first to make sure it is giving the correct results.

I hope this helps and good luck with your code!