What is the error here? Euler Method for 2nd order equations?

Question

Kaylene Widdoes 2016-2-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/268510-what-is-the-error-here-euler-method-for-2nd-order-equations

评论： Torsten 2016-2-18

采纳的回答： Torsten

在 MATLAB Online 中打开

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

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Walter Roberson 2016-2-17

Are you encountering an error message? What do you observe that leads you to be suspicious of the code?

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Answer 1

Torsten 2016-2-17

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/268510-what-is-the-error-here-euler-method-for-2nd-order-equations#answer_210135

在 MATLAB Online 中打开

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