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Euler method is coming up wrong? Help?

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Kaylene Widdoes
Kaylene Widdoes il 17 Feb 2016
Chiuso: Geoff Hayes il 17 Feb 2016
I have the following equation: (x^3)y' + 20*(x^2)y = x with y(2)=0
I have to get the Euler code to run and execute. So far this is my code, but the graph looks wrong, and the approximations aren't even showing up. Any ideas why this may be happening?
Script file:
function[T,Y] = euler(f,a,b,ya,h)
a = 0; b = 1;
T = a:h:b;
Y = zeros(1,length(T));
Y(2) = ya;
for k = 1 : length(T)-1
Y(k+1) = Y(k) + h*f(T(k),Y(k));
end
Code:
%%Part 1 - Euler
% y'(t) = 3*y(t)
% A function file euler.m is needed; you'll do this in the homework
clear all
% define the problem: function f and domain
f = @(t,y) (1/(t^2)) - ((20*y)/t);
a = 2; b = 10;
% exact solution, using a fine grid
t = a:.0001:b;
y = (1./(19.*t)) - (524288./(19.*(t.^20))); % this is a vector of values, not a function
% coarse solution
h = .01;
ya = 0;
[T1,Y1]=euler(f,a,b,ya,h);
% fine solution
h = .001;
ya = 0;
[T2,Y2]=euler(f,a,b,ya,h);
% finer solution
h = .0001;
ya = 0;
[T3,Y3]=euler(f,a,b,ya,h);
plot(t,y,'k',T1,Y1,'bo-',T2,Y2,'ro-',T3,Y3,'go-')
legend('Exact','h=0.01','h=0.001','h=0.001')
title('The Euler Method with 3 meshes')
  1 Commento
Geoff Hayes
Geoff Hayes il 17 Feb 2016
Kaylene - please don't create a duplicate of previously asked questions (<http://www.mathworks.com/matlabcentral/answers/268698-any-ideas-why-euler-method-isn-t-running>).

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