Error in ODE45 when using ...................... >> [t,x] = ode45(@odefcn,tspan,[0 0]);

function dxdt = odefcn(t,x,a,b,c,u)

dxdt = zeros(2,1);
dxdt(1) = a*x(1)+2*x(2)+u;
dxdt(2) = c*x(1)+ b*x(2)-2*u;

end

clc;clear all; close all;
a=-1; b=-2; c=0; u=3;

tspan = [0 20];
[t,x] = ode45(@odefcn,tspan,[0 0]);

figure(1)
plot(t,x(:,1),'r',t,x(:,2),'b')

i am getting an error (attached screenshot)

while i am not getting error when i am using

a=-5; b=-3; c=1; u=3;

tspan = [0 20];
[t,x] = ode45(@(t,x) odefcn(t,x,a,b,c,u),tspan,[0 0]);

figure(2)
plot(t,x(:,1),'r',t,x(:,2),'b')

can anyone please explain

Answer 1

[Walter Roberson]

[t,x] = ode45(@odefcn,tspan,[0 0]);

That is valid syntax.

However, your function is relying on the variables a, b, c, and u. MATLAB never automatically passes variables from the calling environment into a function. If you define

x = 42;
y = f();

and you have defined

function result = f(x)
  result = x.^2;
end

then when you call f without passing any argument into it, MATLAB does not look and see that the internal parameter name for the first argument is x and then look into the script and see there is an x there and use the caller's x as the value for x in the function. That never happens for named parameters. (There are cases where MATLAB will look for a variable in an outer environment, but that is never done for named parameters.)

So... at the time that your function odefcn first needs to use a, b, c, or u, the function would fail, because you would not have passed the values into the function.

The approach you used with the anonymous function

@(t,x) odefcn(t, x, a, b, c, u) 

is the recommended approach. http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

The approach Alan suggested, of instead passing extra parameters, has not been documented since about MATLAB 5.2 or so, and has some subtle internal incompatibilities so it is not completely reliable.

[Md Muzakkir Quamar]

Thank you ...!!

Answer 2

[Alan Stevens]

The first approach needs to be structured as follows:

a=-1; b=-2; c=0; u=3;
tspan = [0 20];
[t,x] = ode45(@odefcn,tspan,[0 0],[],a, b, c, u);
figure(1)
plot(t,x(:,1),'r',t,x(:,2),'b')

function dxdt = odefcn(t,x,a,b,c,u)
dxdt = zeros(2,1);
dxdt(1) = a*x(1)+2*x(2)+u;
dxdt(2) = c*x(1)+ b*x(2)-2*u;
end

[Md Muzakkir Quamar]

if you can please explain if ..

[t,x] = ode45(@odefcn,tspan,[0 0]);

not a valid syntax...? why i am getting an error when i am using this syntax

while there is no error when i am using

[t,x] = ode45(@(t,x) odefcn(t,x,a,b,c,u),tspan,[0 0]);

i need to understand the diff as i have been using the above syntax for many times

[Walter Roberson]

[t,x] = ode45(@odefcn,tspan,[0 0],[],a, b, c, u);

That syntax has not been documented for about 15 years, and there are circumstances under which it can fail. Parameterizing the anonymous function is much better.

[Md Muzakkir Quamar]

but i can see this syntax in Matlab documentation for ODE45 now as well.

[Steven Lord]

That screen shot of the documentation does not show the syntax that Walter stated has not been documented for 15 years, where the additional parameters are passed after the options structure. I second the recommendation not to use this syntax for new code, and if possible to migrate (very) old code to use one of the recommended parameterization techniques.