Solving an ODE when the function is given as discrete values -matlab-

Question

I have the following ODE:

x_dot = 3*x.^0.5-2*x.^1.5  % (Equation 1)

I am using ode45 to solve it. My solution is given as a ve

Answer 1

You can use interp1 to create an interpolated lookup table function:

fx = [0.5644 0.6473 0.7258 0.7999 0.8697 0.9353 0.9967 1.0540 1.1072 1.1564 ...
      1.2016 1.2429 1.2803 1.3138 1.3435 1.3695 1.3917 1.4102 1.4250 1.4362 ...
      1.4438 1.4477 1.4482 1.4450 1.4384 1.4283 1.4147 1.3977 1.3773 1.3535 ...
      1.3263 1.2957 1.2618 1.2246 1.1841 1.1403 1.0932 1.0429 0.9893 0.9325 0.8725];
x = 0:0.25:10
f = @(xq)interp1(x,fx,xq);

Then you should be able to use ode45 as normal:

tspan = [0 1];
x0 = 2;
xout = ode45(@(t,x)f(x),tspan,x0);

Note that you did not specify what values of of x your function (fx here) is evaluated over so I chose zero to ten. You'll also not want to use the copy-and-pasted values from the command window of course because they only have four decimal places of accuracy. Also, note that because ode45 required the inputs t and then x, I created a separate anonymous function using f, but f can created with an unused t input if desired.