How to get values at different interval for ode45

Hello,

I solved a second order differential equation with ode45, the code ran smoothly.

I want to extract the value of the results at different intervals 0:0.1:1.

Is there a way to this in Matlab?

function Shooting_Method
clc;clf;clear;
global C__T R__D S__h Q gamma beta P__e
C__T=0.1;
R__D=0.3;
S__h = 0.1;
Q = 0.4;
gamma = 0.1;
beta = 0.2;
P__e = 1;
x=0.5;
x1=fzero(@solver,x)
end

function F=solver(x)
options=odeset('RelTol', 1e-9, 'AbsTol', [1e-9 1e-9], 'OutputFcn', @odeplot);
[t,u] = ode45(@equation, [0 1], [x,0], options);
s=length(t);
F=u(s,1)-1;
figure(1)
plot(t,u(:,1))
end

function dy = equation(t,y)
global C__T R__D S__h Q gamma beta P__e
dy=zeros(2,1);
dy(1) = y(2);
dy(2) = ((4 * C__T ^ 3 * y(1) * R__D) + (6 * C__T ^ 2 * R__D * y(1) ^ 2)+...
    (4 * C__T * R__D * y(1) ^ 3) + (y(1) ^ 4 * R__D) - S__h * Q * gamma...
    * y(1) - beta * y(2) ^ 2 + S__h * (y(1) ^ 2) + P__e * y(2) - S__h * Q)...
    / (beta * y(1) + 0.1e1);
end

Answer 1

[darova]

Use for loop to get results for x = 0: 0.1: 1 (11 curves)

hold on
for x = 0:0.1:1
	[t,u] = ode45(@equation, [0 1], [x 0])
	plot(t,u(:,1))
end
hold off

[Mayokun Ojediran]

@darova I am not trying to solve for different values of x, I am trying to display the results for u for different values of t. Thank you

[darova]

There two ways to do this

First one

tspan = 0:0.1:1;
[t,u] = ode45(@equation, tspan, [x 0])
plot(t,u(:,1))

Second one

[t,u] = ode45(@equation, [0 1], [x 0])
t1 = 0:0.1:1;
u1 = interp1(t,u(:,1),t1);
plot(t,u(:,1))                    % ode45 data
hold on
plot(t1,u1,'.r')                  % data at specific points
hold off