MATLAB: How to improve the euler code

euler

How can i improve my euler code? Code is attached … I believe i have to improve it by using trapezoids instead of rectangles..How do i do this ? Can someone help

Best Answer

For trapezoidal integration, you use the average of two consecutive evaluations. This could be done by simply adding one line of code after the Euler calculation;

 y(:,k+1) = (y(:,k+1) + y(:,k))*h/2

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MATLAB: Coding Euler’s Method!!

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')

MATLAB: Runge Kutta 4th order

Your code seems to have some issues. Try this one:

h = pi/10;
x = 0 : h : 2*pi;
n = length(x);
y = zeros(2,n);
y(:,1) = [0, 0.25];
for k = 1: (n-1)
                k1 = h * rung(x(k), y(:,k)); 
                k2 = h * rung(x(k)+h/2, y(:,k) + k1/2);
                k3 = h * rung(x(k)+h/2, y(:,k) + k2/2);
                k4 = h * rung(x(k)+h, y(:,k) + k3);
                y(:,k+1) = y(:,k) + (k1 + 2*k2 + 2*k3 + k4)/6;
end
subplot(211); plot(x, y(1,:))
subplot(212); plot(x, y(2,:))
function f = rung(x,y)
    f(1,1) = y(2); 
    f(2,1) = -0.03*x*y(2) - y(1);
end

Best Answer

Related Solutions

MATLAB: Coding Euler’s Method!!

MATLAB: Runge Kutta 4th order

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