2nd order ode using euler method

The following second-order ODE is considered to be stiff: d2y/dx2=−1001dy/dx−1000?

initial conditions are: y(0)=1 and ?′(0)=0

What to solve the ODE using Euler’s method with implicit function.

I implemetd the above question using matlab. But implemented code gives this error.

I attached the code. Can anyone suggest me about the bug of this code?.

function dy = dpnon(t, y)
dy = [y(2);-1000*y(1)-1001*y(2)];
end

function [x,y]=euler_explicit(f,xinit,yinit,xfinal,h)
n=(xfinal-xinit)/h;

% Initialization of x and y as column vectors
x=[xinit zeros(1,n)]; y=[yinit zeros(1,n)];

% Calculation of x and y
for i=1:n
x(i+1)=x(i)+h;
y(i+1)=y(i)+h*f(x(i),y(i));
end
end

xinit=0;
xfinal=3;
yinit=0;
h=.5;
euler_explicit(@dpnon,xinit,yinit,xfinal,h)

Answer 1

[Torsten]

function main
  xinit = 0;
  xfinal = 3;
  yinit = [1 0];
  h = .5;
  [x,y] = euler_explicit(@dpnon,xinit,yinit,xfinal,h)
  plot(x,y(:,1))
end


function [x,y]=euler_explicit(f,xinit,yinit,xfinal,h)
  n = (xfinal-xinit)/h;

  % Initialization of x and y as column vectors
  x = [xinit;zeros(n,1)];
  y = [yinit;zeros(n,2)];

  % Calculation of x and y
  for i = 1:n
    x(i+1) = x(i) + h;
    y(i+1,:) = y(i,:) + h*f(x(i),y(i,:));
  end
end

function dy = dpnon(t, y)
  dy = [y(2),-1000*y(1)-1001*y(2)];
end