title: Solving an ODE when the function is given as discrete values -matlab-
body: <p>I have the following ODE:</p>
  
  <pre><code>x_dot = 3*x.^0.5-2*x.^1.5  % (Equation 1)
  </code></pre>
  
  <p>I am using <code>ode45</code> to solve it. My solution is given as a vector of dim(k x 1) (usually k = 41, which is given by the <code>tspan</code>).</p>
  
  <p>On the other hand, I have made a model that approximates the model from (1), but in order to compare how accurate this second model is, I want to solve it (solve the second ODE) by means of <code>ode45</code>. My problem is that this second ode is given discrete:</p>
  
  <pre><code>x_dot = f(x) % (Equation 2)
  </code></pre>
  
  <p><code>f</code> is discrete and not a continuous function like in (1). The values I have for <code>f</code> are: </p>
  
  <pre><code>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
  </code></pre>
  
  <p>What I want now is to solve this second ode using <code>ode45</code>. Hopefully I will get a solution very similar that the one from (1). How can I solve a discrete ode applying <code>ode45</code>? Is it possible to use <code>ode45</code>? Otherwise I can use <code>Runge-Kutta</code> but I want to be fair comparing the two methods, which means that I have to solve them by the same way.</p>