What is the error here? Euler Method for 2nd order equations?
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I have the following files and script file, but the graph is definitely wrong for the approximations. Any ideas?
Code:
clear all
% define the problem: function f and domain
f = @(t,y) (0*t+3*y);
a = 0; b = 1;
% exact solution, using a fine grid
t = a:.0001:b;
y = exp(3*t); % this is a vector of values, not a function
% coarse solution
h = .25;
ya = 1;
[T1,Y1]=euler(f,a,b,ya,h);
% fine solution
h = .05;
ya = 1;
[T2,Y2]=euler(f,a,b,ya,h);
% finer solution
h = .01;
ya = 1;
[T3,Y3]=euler(f,a,b,ya,h);
plot(t,y,'k',T1,Y1,'bo-',T2,Y2,'ro-',T3,Y3,'go-')
legend('Exact','h=0.25','h=0.05','h=0.01')
title('The Euler Method with 3 meshes')
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(1) = a;
for k = 1 : length(T)-1
Y(k+1) = Y(k) + h*f(T(k),Y(k));
end
1 Comment
Walter Roberson
on 17 Feb 2016
Are you encountering an error message? What do you observe that leads you to be suspicious of the code?
Accepted Answer
Torsten
on 17 Feb 2016
function[T,Y] = euler(f,a,b,ya,h)
a = 0; b = 1;
T = a:h:b;
Y = zeros(1,length(T));
*Y(1) = ya;*
for k = 1 : length(T)-1
Y(k+1) = Y(k) + h*f(T(k),Y(k));
end
Best wishes
Torsten.
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