Need help using ODE45 and eulers function

조회 수: 38 (최근 30일)
Chris
Chris 2013년 11월 5일
답변: Jonathan LeSage 2013년 11월 5일
Alright so I have this ODE I solved for it using ODE45 and now its asking me to modify my script by using a eulers method script that was given to us and use eulers to solve for it now. I am lost. If its confusinf at all let me know and i can try to clarify it.
Here is my ODE file
function ex_with_2eqs
t0 = 0; tf = 40; y0 = [-1;0];
[t,Y] = ode45(@f,[t0,tf],y0,[]);
y = Y(:,1);
v = Y(:,2);
figure(1);
plot(t,y,'b+',t,v,'ro')
legend('y(t)','v(t)=y''(t)');
title('Figure 1 L4g');
grid on;
ylim([-1.5,1.5]);
figure(2);
plot(y,v); axis square; xlabel('y'); ylabel('v');
title('Figure 2 L4g phase plot');
grid on;
ylim([-1.5,1.5]);
xlim([-1,1]);
end
Here is my function file
function dydt = f(t,Y)
y = Y(1);
v = Y(2);
dydt = [ v; cos(t)-4*y^2*v-3*y ];
end
and if it matters here is my eulers file although i know i dont have to do anything with it.
f
unction [te,Ye] = euler(f,tspan,y0,N)
% Solves the IVP y' = f(t,y), y(t0) = y0 in the time interval tspan = [t0,tf]
% using Euler's method with N time steps.
% Input:
% f = name of inline function or function M-file that evaluates the ODE
% (if not an inline function, use: euler(@f,tspan,y0,N))
% For a system, the f must be given as column vector.
% tspan = [t0, tf] where t0 = initial time value and tf = final time value
% y0 = initial value of the dependent variable. If solving a system,
% initial conditions must be given as a vector.
% N = number of steps used.
% Output:
% t = vector of time values where the solution was computed
% y = vector of computed solution values.
m = length(y0);
t0 = tspan(1);
tf = tspan(2);
h = (tf-t0)/N; % evaluate the time step size
t = linspace(t0,tf,N+1); % create the vector of t values
y = zeros(m,N+1); % allocate memory for the output y
y(:,1) = y0'; % set initial condition
for n=1:N
y(:,n+1) = y(:,n) + h*f(t(n),y(:,n)); % implement Euler's method
end
t = t'; y = y'; % change t and y from row to column vectors
end

답변 (1개)

Jonathan LeSage
Jonathan LeSage 2013년 11월 5일
It looks to me that you're nearly there! I found a couple of small mistakes that seems to be holding you back.
Changes to your code:
  • Replace ode45 with you defined euler function
  • Read the documentation of your euler function. Unlike ode45 which is a variable step numerical solver, Euler's method is a fixed step solver. As such, you need to specify the number of steps you want to take, N, as the final fuction input. I would imagine 250+ steps would be sufficient for this problem.
Changes to your euler function:
  • The two outputs of the function [te,Ye] are never defined in the code. From what I can tell, the outputs should be changes to [t,y].
Hope this helps to rectify the problem!

카테고리

Help CenterFile Exchange에서 Ordinary Differential Equations에 대해 자세히 알아보기

Community Treasure Hunt

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

Start Hunting!

Translated by