2nd degree ODE with ode45

2012 5 24
1 个回答
4 次查看（30 天）

0 个投票

Hello everybody,
this is a great occasion to explain MATLAB's ODE solving strategies to less experienced users like me.
I'm trying to solve a 2nd degree ODE u'' = (1/t)*u' - 4*(t^2)*u with ode45; on [1,20].
Inspired by the documentation for ode45, I tried:
function dy = rigid(x,y)
function ddy = rigid(x,dy)
dy = @(x) diff(y)
ddy = @(x) (1/x)*dy(x) - 4*(x^2)*y(x)
tspan = [1 20]
y0 = [sin(1)+cos(1); 1*cos(1)-1*sin(1)]
[X,Y] = ode45(@rigid,tspan,y0)
plot(X,Y)
which my MATLAB accepts without error messages, but doesn't produce any plot. Could you give me a hint what could be wrong?
Thank you!

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回答（1 个）

bym
bym 2012-5-24

2 个投票

Well, pretty close. You need to define the ODE as a system of first order ODE's realizing the function arguments can be a matrix (example without using anonymous functions):
function dudt = rigid(t,x)
dudt = [x(2);x(2)./t-4.*t.^2*x(1)]; % function named rigid.m
in the script you would then use
tspan = [1 20];
y0 = [sin(1)+cos(1); 1*cos(1)-1*sin(1)];
[X,Y] = ode45(@rigid,tspan,y0);
plot(X,Y);

4 个评论
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Nina
Nina 2012-5-25
Thank you! It makes, sense, now, at least, I'm getting an error message, but now, I really don't understand what's the problem.
function du = rigid(t,u)
du = zeros(3,1); %a column vector
du(1) = du(3)./4.*(t^2) - (t.^(-3))*du(2); %this is line 5
du(2) = @(t) du(3).*t + du(1)*4.*(t.^3)
du(3) = @(t) du(2)./t - du(1)*(4.*t.^2)
[T,U] = ode45(@rigid,[1 20],[sin(1)+cos(1) cos(1)-sin(1) -3*cos(1)-5*sin(1)]);
plot(T,U)
Matlab response is "Error using Ch16Pr20b (line 5)
Not enough input arguments."
Do you know what could be the missing argument?
Nina
Nina 2012-5-25
Actually, a more simple code would be
function xdot = fun1(t,x);
xdot(2) = (1/t)* x(2) - 4*t.^2* x(1);
xdot(1) = x(2);
xdot=xdot(:);
X0 = [sin(1)+cos(1) cos(1)-sin(1) -3*cos(1)-5*sin(1)];
t0 = 1;
tf = 20;
options = [];
[t,y] = ode45(@fun1, [t0,tf],X0, options);
plot(t,y)
But the error message remains the same: not enough input arguments...
Sean de Wolski
Sean de Wolski 2012-5-25
I don't know about the error but you're not going to be able to stack two anonymous functions into a vector du. You will get and error on lines 6/7 for trying this.
Walter Roberson
Walter Roberson 2012-5-25
Storing anonymous functions in [object] vectors used to be supported (but not in numeric vectors). But it led to ambiguous syntax, so now one is required to use cell arrays to store anonymous functions.

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Nina
Nina
2012-5-24

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