如何在 Collimator 中实现欧拉函数？

Question

你能帮我在 Collimator 中实现这个欧拉函数吗？

function [t,y] = MyEuler(f,tinterval,y0,n)
  y = zeros(n+1,1) // y vector of zeroes 
  y(1) = y0    //y0 is the first element of the y vector
  dt = (tinterval(2)-tinterval(1))/n  //step size
  //disp('dt')
  t = tinterval(1):dt:tinterval(2)   
  for i = 1:n
      y(i+1) = y(i)+f(t(i),y(i))*dt
  end
  t = t'        
endfunction ```

Answer 1

您的编写几乎正确，几乎没有语法错误，因此这是一个没有任何错误的重新访问版本。

function [t, y] = MyEuler(f, tinterval, y0, n)
   % Initialize the vector of zeros for y
   y = zeros(n+1, 1); % y vector of zeroes
   y(1) = y0;         % y0 is the first element of the y vector

   % Calculate the step size
   dt = (tinterval(2) - tinterval(1)) / n;

   % Create the time vector t
   t = linspace(tinterval(1), tinterval(2), n+1);

   % Euler's method loop
   for i = 1:n
      y(i+1) = y(i) + f(t(i), y(i)) * dt;
   end

   % Transpose t to ensure it matches the output format
   t = t';
end

这是运行上述函数的测试代码

% Define the differential equation dy/dt = y - t^2 + 1
f = @(t, y) y - t^2 + 1;

% Set the time interval [t0, tf], initial condition y0, and number of  steps n
tinterval = [0, 2];
y0 = 0.5;
n = 10;

% Call the MyEuler function
[t, y] = MyEuler(f, tinterval, y0, n);