MATLAB: Ode45 is not evluated at requried interval

Question

Greetings,

I'm trying to run the following code for solving the linear 2nd order ODE y''=y+1; for 0<=x<=10, with boundary condituions y(0)=1, y(10)=0, and a step size of h=0.01. I give only the first part of the code, because this is where I face this issue.

The code was pretty much used as is from this page : https://www.mathworks.com/help/symbolic/odetovectorfield.html#bvlvtw5-1

*——–*

clear all; clc;

h=0.01;

xspan=[0:h:10];

y1=[1 1];

syms y(x)

[V] = odeToVectorField(diff(y, 2) == (y+1));

M = @(x,Y)[Y(2); Y(1)+1];

sol1=ode45(M,xspan,y1);

*——–*

the solution I get is:

*——–*

sol1 =

struct with fields:

solver: 'ode45'

extdata: [1×1 struct]

x: [0 0.0100 0.0600 0.3100 1.1195 2.1035 3.1035 4.1035 5.1035 6.1035 7.1035 8.1035 9.1035 10]

y: [2×14 double]

stats: [1×1 struct]

idata: [1×1 struct]

*——–*

The question is why the resulting y vector is solved for the given x and not in the intervals I specified in xspan?

I know ode45 solves for its own step size, but as far as I understand it is still supposed to be evaluated in the intreval above mentioned

Thanks so much in advance

Michael

Answer 1

Hi,

you get this if you specify the ode45 call this way:

[x, y]=ode45(M,xspan,y1);

Note that this forces Matlab to calculate much more points as needed with respect to a solution inside the tolerance range.

Best regards

Stephan