Coding Euler's Method!!

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Sharif
Sharif 2014-11-8
回答： Mohammad Abouali 2014-11-9
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!
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Sharif
Sharif 2014-11-8
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
Sharif 2014-11-9
Anybody think they can help? :\

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Mohammad Abouali
Mohammad Abouali 2014-11-9
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')

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