Second Order ODE solved with ODE45

2 次查看(过去 30 天)
Hi!
I am struggling with the task to solve a 2'nd order Ode with ODE45. Please help as I'm struggling with this.
Equation as given in the task:
y'' + pi*y^(x/3)*(2y' sin pi*x + pi*y cos pi*x) − y/9 = 0, y(0) = and y'(0) = -⅓
My code:
%Lab 2 uppgift 3
clear all
close all
clc
[t,y] = ode45(@odefun, t, [0, 2.5], [1, -1/3]);
plot(t,y(:,1),'-',t,y(:,2),'--')
title('Title');
xlabel('time t');
ylabel('solution y');
legend('y_1','y_2')
%The function called odefun.
function [dydx] = odefun(t,y)
%x = (0:0.1:2.5);
dydt=[y(2); pi*y(1).*exp(x/3)*2*y(2)*sin(pi*x) + x*y(1)*cos(pi*x) - (y(1)./9)x];
end
Thanks! /Henrik

采纳的回答

Star Strider
Star Strider 2014-10-25
Your equation implies (to me) that y is a function of x, not t. So your function should probably be:
function [dydx] = odefun(x,y)
Also, there is an error in this line at the very end:
dydt=[y(2); pi*y(1).*exp(x/3)*2*y(2)*sin(pi*x) + x*y(1)*cos(pi*x) - (y(1)./9)x];
You might want:
dydt=[y(2); pi*y(1).*exp(x/3)*2*y(2)*sin(pi*x) + x*y(1)*cos(pi*x) - (y(1)./9).*x];
or some other operator, since MATLAB will throw an error without an operator there.
When I ran it (with the change in the function line, vectorising, and putting a multiplication operator before the x at the end, it ran.
  2 个评论
Henrik
Henrik 2014-10-25
Thanks a lot star strider!
The plot I get doesn't look right but I get it running at least. However with an error message saying:
"Warning: Failure at t=1.425454e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (3.552714e-15) at time t."
If you have any ideas to get rid of it I'm even more grateful.
Thanks //Henrik
Star Strider
Star Strider 2014-10-25
My pleasure!
I re-coded your equation and found some errors. This seems to produce a much more reasonable result:
odefun = @(x,y) [y(2); -pi*y(1).^(x/3).*2.*y(2).*sin(pi*x) - x.*y(1).*cos(pi*x) + (y(1)./9).*x];
[t,y] = ode15s(odefun, [0, 2.5], [1, -1/3]);
plot(t,y(:,1),'-',t,y(:,2),'--')
title('Title');
xlabel('time t');
ylabel('solution y');
legend('y_1','y_2','Location','NW')
I also repositioned your legend so that it would not be on top of your plotted curves.

请先登录,再进行评论。

更多回答(0 个)

类别

Help CenterFile Exchange 中查找有关 Ordinary Differential Equations 的更多信息

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by