Input argument for ode45 function type error

I am trying to modify the following code.

tspan = [0 10];
x0 = 0;
[t,x] = ode45(@(t,x) (-4.76e+1*x^2 + 5.69e-9*x + 7.98e-2)/(1.67e+4*x + 1.12), tspan, x0);
plot(t,x,'b')
xlim([0 0.001])

The input argument to the ode45 function is directly typed in. If instead you write it as

tspan = [0 10];
x0 = 0;
f = (-4.76e+1*x^2 + 5.69e-9*x + 7.98e-2)/(1.67e+4*x + 1.12); 
[t,x] = ode45(@(t,x) f, tspan, x0);
plot(t,x,'b')
xlim([0 0.001])

then there is an error, even though the type of the argument is the same. Can anyone explain how the argument can be input as a variable that stores the expression?

Answer 1

[Star Strider]

Yes.

Create it as an anonymous function at the outset —

tspan = [0 10];
x0 = 0;
f = @(t,x) (-4.76e+1*x^2 + 5.69e-9*x + 7.98e-2)/(1.67e+4*x + 1.12); 
[t,x] = ode45(f, tspan, x0);

figure
plot(t,x,'b')
grid
xlim([0 0.001])

.

[Aleem Andrew]

Thank you for your help. The problem I was encountering is that I wanted to plot a symbolic expression using ode45 and the argument must be a function handle, so I converted the symbolic expression using matlabFunction but although it was converted to a function handle I still got an error.

syms x
f = (- 4.76e+67*x^2 + 5.69e+57*x + 7.98e+64)/(1.67e+70*x + 1.12e+66)
f = matlabFunction(f) 
tspan = [0 10];
x0 = 0; 
[t,x] = ode45(f, tspan, x0);
plot(t,x,'b')
grid
xlim([0 0.001])

How do you convert a symbolic expression like f to the appropriate type to be plotted using ode45?

[Star Strider]

As always, my pleasure!

It is necessary to include the 'Vars' optional argument to matlabFucntion to get the correct result —

syms x t 
f = (- 4.76e+67*x^2 + 5.69e+57*x + 7.98e+64)/(1.67e+70*x + 1.12e+66)

f = 

f = matlabFunction(f, 'Vars',{t,x}) 

f = function_handle with value:
    @(t,x)(x.*5.69e+57-x.^2.*4.76e+67+7.98e+64)./(x.*1.67e+70+1.12e+66)

tspan = [0 10];
x0 = 0; 
[t,x] = ode45(f, tspan, x0);
plot(t,x,'b')
grid
xlim([0 0.001])

Using 'Vars' so that the created function is of both ‘t’ and ‘x’ (and in the specified order of the ‘Vars’ matching value) creates a function that ode45 and the others can use.

Note — This also requries adding ‘t’ to the syms declaration.

.

[Aleem Andrew]

Thank you, I appreciate your help

[Star Strider]

As always, my pleasure!

.