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Euler method is coming up wrong? Help?

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Kaylene Widdoes
Kaylene Widdoes 2016-2-17
关闭： Geoff Hayes 2016-2-17
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 个评论
Geoff Hayes
Geoff Hayes 2016-2-17
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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