Some trouble with difference equations

Question

paul 2012-2-15

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/29249-some-trouble-with-difference-equations

关闭： MATLAB Answer Bot 2021-8-20

在 MATLAB Online 中打开

Hey,

I'm not a heavy matlab user and started programming on ml this weak...

I've got the following problem (whicht i can't solve despite heavy use of google):

I got the following equation system which i want to solve nummeric over time

r(t)=-a_r-b_r*y(t-1)-c_r*ir(t-1)-d_r*lamda(t-1)+r(t-1)
y(t)=a_y+b_y*(ir(t)-pi(t))+c_y*r(t)
pi(t)=a_pi+b_pi*y(t)+c_pi*r(t)
ir(t)=a_i+b_i*y(t)+c_i*pi(t)+d_i*r(t)+e_i*lamda(t)
lamda(t)=a_l+b_l*y(t)+c_l*ir(t)+d_l*pi(t)

the variables indicated with t are the one of interest and start values are given...

the variables a,b,c,d,e are constant coefficients given as well... The problem is to solve for one period and then in the next step for arbitraly many.

I have tried with loops (the problem was to integrate the break condition properly) and fsolve (here i failed to add time index) but came to no conclusion.

I would be very gratefully for any help

lg

2 个评论
显示无隐藏无

Andrew Newell 2012-2-15

What are your starting values for r, y, etc.?

Andrew Newell 2012-2-15

What is your criterion for stopping? Is it a fixed number of time intervals, e.g., 0, dt, 2*dt, ..., n*dt - or perhaps convergence?

此问题已关闭。

Answer 1

Rick Rosson 2012-2-16

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/29249-some-trouble-with-difference-equations#answer_37618

在 MATLAB Online 中打开

Please try:

   % Number of time steps:
   M = 200;
   % Number of state variables:
   N = 5;
   % Pre-allocate data array:
   x = zeros(M,N);
   % Coefficients for difference equations:
   a = [ ... ];
   b = [ ... ];
   c = [ ... ];
   d = [ ... ];
   % List of names for the state variables:
   varNames = { 'r'   'y'  'pi'  'ir'  'lambda'  };
   % Time increment:
   dt = ... ;   % <---- replace ... with desired value
   % Time domain:
   t = dt*(0:M-1)';
   % Initial values:
   x(1,:) = [ ... ];   % <---- replace ... with five initial values
   % Main Loop - update state variables using difference equations:
   for k = 2:M
       x(k,1) = ... ;
       x(k,2) = ... ;
       x(k,3) = ... ;
       ...
       ...
   end
   % Plot results:
   figure;
   plot(t,x(:,1));
   title(varNames{1});

HTH.

6 个评论
显示 4更早的评论隐藏 4更早的评论

Rick Rosson 2012-2-16

Yes, Walter makes several good points. The code I posted is meant to provide a template that you can use as a starting point. Once you get something that works, you can tweak the code for speed, memory, precision, convergence rate, etc.