Trouble with Euler's method in MATLAB

[Malby]

I'm trying to solve an ODE using MATLAB and Euler's method but I've having some trouble understanding what's going on with the code. This is something relatively simple but I'm new to MATLAB so I'm not really sure what's going on.

The question:

Write a Matlab M-file that uses Euler’s method to numerically solve the IVP: dy/dt = y, y(1859) = 12. Solve the IVP up to the year 1864 using a step size of 0.1 years. This is modelling the exponential growth of rabbits in Australia for five years from the introduction of 12 rabbits at the start of 1859.

We are then given this code as an example:

t=0:0.5:5;
y(1)=1;
for i = 1:10
y(i+1)=y(i)+t(i)^2*0.5;
end
plot(t,y,’b:’)
hold on
yexact = t.^3/3+1;
plot(t,yexact,’r--’)
legend(’Numerical solution’, ’Analytical solution’);
title(’Example IVP solution’)
xlabel(’t’)
ylabel(’y’)

I used that code and then modified in in a way which I thought would give me what I need, for the first part anyway (without the labelling etc.):

clear all
t=1859:0.1:1864;
y(1)=12;
for i = 1:50
y(i+1)=y(i)+y(i)*0.1;
end
y(50)
plot(t,y,'-')

However this isn't giving me what I need.

Any suggestions would be greatly appreciated.

 

[NateD]

The code you provided is an example of solving an IVP using Euler's method. To solve the problem you have given, you need to modify it accordingly. First, you need to set the initial conditions. In your example, the initial condition is y(1) = 12. Second, you need to set the time step. In your example, the time step is 0.1 years. Third, you need to define the right-hand side of the equation. In your example, the right-hand side is dy/dt = y.Finally, you need to set the range of values for t. In your example, this is from 1859 to 1864.Using these parameters, you can write the following code:clear allt=1859:0.1:1864;y(1)=12;for i = 1:50 y(i+1)=y(i)+y(i)*0.1;endy(50)plot(t,y,'-')