euler

function euler_T

  % y' = (-y+x*sin(x))/x; y(1) = 0.3011687, x = [1, 2]

  X = [1, 2];
  y0 = 0.3011687;
  h1 = 0.1;
  h2 = 0.01;

  y_me1 = euler_method(X, y0, h1);
  y_me2 = euler_method(X, y0, h2);

  y_mi1 = euler_midpoint(X, y0, h1);
  y_mi2 = euler_midpoint(X, y0, h2);

  i = 1;
  printf('\n  I \n\n h1 = 0.1 \n\n  X   Y');
  for j = X(1):h1:X(2)
    printf('\n  %i   %i', j, y_me1(i));
    i += 1;
  endfor

  i = 1;
  printf('\n\n  h2 = 0.01 \n');
  for j = X(1):h2:X(2)
    printf('\n  %i   %i', j, y_me2(i));
    i += 1;
  endfor

  i = 1;
  printf('\n\n\n  II \n\n h1 = 0.1 \n\n');
  for j = X(1):h1:X(2)
    printf('\n  %i   %i', j, y_mi1(i));
    i += 1;
  endfor

  i = 1;
  printf('\n\n  h2 = 0.01 \n');
  for j = X(1):h2:X(2)
    printf('\n  %i   %i', j, y_mi2(i));
    i += 1;
  endfor


  plot(X(1):h1:X(2), y_me1(1:end-1), 'r', X(1):h2:X(2), y_me2(1:end-1), 'b', X(1):h1:X(2), y_mi1, 'g', X(1):h2:X(2), y_mi2, 'y');
    title('    red - h1; blue - h2, green - h1 & pereschet, yellow - h2 & pereschet   '), grid on



end



function y = euler_method(X, y_i, h)
  y = [y_i];
  i = 1;

  for x = X(1):h:X(2)

    y(i+1) = y(i) + h*f(x, y(i));
    i += 1;

  endfor

endfunction


function y = euler_midpoint(X, y_i, h)
  y = [y_i];
  i = 1;

  for x = X(1):h:X(2)-h

    y(i+1) = y(i) + h/2*( f(x, y(i)) + f(x+h, y(i) + h*f(x, y(i))) );
    i += 1;

  endfor

endfunction


function f = f(x, y)

  f = (-y + x*sin(x)) / x;

endfunction