MATLAB: Euler method Subroutine, Euler portion provided

eulereuler methodsubroutine

I have been provided the code below to solve an ODE using Euler's Method. I am unsure how to write the subroutine to implement this code to find a solution.

CODE:

function [X,Y]= euler(f,x_o,x_f,y_o,N)
  if N<2
      N=2;
  end
  h=(x_f-x_o)/N;
  X=zeros(N+1,1);
  M=max(size(y_o));
  Y=zeros(N+1,M);
  
    x=x_o;  X(1)=x;  y=y_o; Y(1,:)=y';
    
    for i=1:N
        k1=h*feval(f,x,y);
        y=y+k1;
        x=x+h;
        X(i+1)=x;
        Y(i+1,:)=y';
    end
end

Best Answer

Download the zip file given in this answer: https://www.mathworks.com/matlabcentral/answers/98293-is-there-a-fixed-step-ordinary-differential-equation-ode-solver-in-matlab-8-0-r2012b#answer_107643 and study the code of ode1.m. It is the implementation of the Euler method provided in very early releases of MATLAB. It is no longer included in MATLAB, but it is still useful to understand the implementation of the Euler method.

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MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

Here's a version:

% Initial conditions
t0=0;
x0=0:0.2:1;
y0=1:0.2:2;
dt=0.1;
tz=1;
t_range= t0:dt:tz;
X = zeros(numel(x0),numel(t_range));
Y = zeros(numel(y0),numel(t_range));
x_rk=zeros(1,numel(t_range));
y_rk= zeros(1,numel(t_range));
for n = 1:numel(x0)
    x_rk(1)=x0(n);
    y_rk(1)=y0(n);
    for i=1:length(t_range)-1
        [x_rk(i+1), y_rk(i+1)]=rk_method(x_rk(i),y_rk(i),dt);
    end
    X(n,:) = x_rk;
    Y(n,:) = y_rk;
    %% PLots
    subplot(numel(x0)/2,2,n)
    plot (t_range, x_rk,'b-o',t_range, y_rk,'y-o','MarkerSize',5);
    grid
    title([num2str(x0(n)),'   ',num2str(y0(n))])
    legend('x','y')
end
disp('X = '), disp(X)
disp('Y = '), disp(Y)
%% Functions
function [dxdt, dydt]= f(x,y)
dxdt =  5*x-3*y;
dydt = -6*x+2*y;
end 
function [x1, y1]=rk_method(x0,y0,dt)
[k11, k12]=f(x0,y0);     
[k21, k22]=f(x0+0.5*dt*k11,y0+0.5*dt*k12); 
[k31, k32]=f(x0+0.5*dt*k21,y0+0.5*dt*k22); 
[k41, k42]=f(x0+dt*k31, y0+dt*k32); 
x1=x0+dt*((k11/6)+((k21+k31)/3)+(k41/6));
y1=y0+dt*((k12/6)+((k22+k32)/3)+(k42/6));
end

MATLAB: Euler’s Method

There is a parentheses mismatch in your code for the euler's method.

Replace that line with:

y(i+1) = y(i) + h *(sin(x) * ( 1 - y(i))) ; %Euler's Method

Best Answer

Related Solutions

MATLAB: 4th order Runge-Kutta code that can solve for several intial conditions

MATLAB: Euler’s Method

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