Coding Euler's Method!!

Hello everyone so I am trying to code Euler's method to solve this matrix A and I can't figure it out. Here is my code so far:

k_AB = 0.4;
k_BC = 0.1;
k_CA = 0.4;
k_ba = 0.2;
k_cb = 0.45;
k_ac = 0.16;

A = [ (-k_AB - k_ac), k_ba, k_CA;
      k_AB, (-k_BC - k_ba), k_cb;
      k_ac, k_BC, (-k_CA - k_cb); ];

x0 = [1;0;0];

h = 0.1;

for t = 0:0.1:1

     xNEW = x0 + h*(A*x0);

      x0 = xNEW

end

x0 = [2;0;0];

It seems that my first step has the 3 correct values, but every step after that is incorrect. If anyone who is familiar with Euler's Explicit Method can help I'd be extremely grateful! I've been trying this for hours on my Friday night :(

So step size = 0.1, initial conditions = [1;0;0] from time interval 0:0.1:1

Any help works!

[James Tursa]

Why do you think other steps are incorrect? Are all the elements correct with the derivative matrix A?

[Sharif]

I tried solving it by hand and trust my hand-written answers more than my MATLAB code. And can you elaborate about what you said about the derivative of matrix A?

[Sharif]

Anybody think they can help? :\

Answer 1

[Mohammad Abouali]

Your code is correct. What is x0 = [2;0;0]; at the end though.

Here is a modified version of your code. It is modified in such a way that you plot the changes in time at the end for each element of x

clear;
clc;
close all;
k_AB = 0.4;
k_BC = 0.1;
k_CA = 0.4;
k_ba = 0.2;
k_cb = 0.45;
k_ac = 0.16;
A = [ (-k_AB - k_ac), k_ba, k_CA;
      k_AB, (-k_BC - k_ba), k_cb;
      k_ac, k_BC, (-k_CA - k_cb); ];
x(:,1) = [1;0;0];
h = 0.1;
t=0:h:1;
for i=2:numel(t)
     x(:,i) = x(:,i-1) + h*(A*x(:,i-1));
end
plot(t,x(1,:),'b')
hold on
plot(t,x(2,:),'r')
plot(t,x(3,:),'k')
xlabel('Time')