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  3. Fail:Wave equation 1D fixed endpoints.gif - Wikipedia Bahasa Melayu, ensiklopedia bebas
Fail:Wave equation 1D fixed endpoints.gif - Wikipedia Bahasa Melayu, ensiklopedia bebas
Daripada Wikipedia, ensiklopedia bebas.

Wave_equation_1D_fixed_endpoints.gif (274 × 121 piksel, saiz fail: 129 KB, jenis MIME: image/gif, berulang, 99 bingkai, 4.9 s)

Fail ini dari Wikimedia Commons dan mungkin digunakan oleh projek lain. Penerangan pada laman penerangan failnya di sana ditunjukkan di bawah.

Keterangan
English: Illustration of solution of one-dimensional wave equation: a gaussian wave on a string fixed at both ends. The wave reflects from each end with a 180° phase shift.
Tarikh (UTC)
Sumber self-made, with en:Matlab
Pengarang Oleg Alexandrov
 
This diagram was created with MATLAB.
Public domain Saya selaku pemegang hak cipta karya ini melepaskan karya ini ke dalam domain awam di seluruh dunia.
Di sesetengah negara, undang-undangnya mungkin tidak mengizinkan; jika begitu:
Saya memberi sesiapa sahaja hak untuk menggunakan karya ini untuk apa jua tujuan, tanpa sebarang syarat, melainkan undang-undang menetapkan syarat-syarat sedemikian.

MATLAB source code

% A wave travelling on a string with
% fixed endpoints

function main()

   % KSmrq's colors
   red    = [0.867 0.06 0.14];
   blue   = [0, 129, 205]/256;
   green  = [0, 200,  70]/256;
   yellow = [254, 194,   0]/256;
   white = 0.99*[1, 1, 1];
   
   % length of the string and the grid
   L = 5;
   N = 151;
   X=linspace(0, L, N);

   h = X(2)-X(1); % space grid size
   c = 0.5; % speed of the wave
   tau = 0.25*h/c; % time grid size
   
   K = 5; % steepness of the bump
   S = 0; % shift the wave
   f=inline('exp(-K*(x-S).^2)', 'x', 'S', 'K'); % a gaussian as an initial wave
   df=inline('-2*K*(x-S).*exp(-K*(x-S).^2)', 'x', 'S', 'K'); % derivative of f

   % wave at time 0 and tau
   U0 = 0*f(X, S, K);
   U1 = U0 - 2*tau*c*df(X, S, K);
   
   U = 0*U0; % current U

   Big=10000;
   Ut = zeros(Big, N);
   Ut(1, :) = U0;
   Ut(2, :) = U1;
   
   % hack to capture the first period of the wave
   min_k = 2*N; k_old = min_k; turn_on = 0;

   for j=3:Big

      last_j = j;
      
      %  fixed end points
      U(1)=0; U(N)=0;
      
      % finite difference discretization in time
      for i=2:(N-1)
         U(i) = (c*tau/h)^2*(U1(i+1)-2*U1(i)+U1(i-1)) + 2*U1(i) - U0(i);
      end

      Ut(j, :) = U;
      
      % update info, for the next iteration
      U0 = U1; U1 = U;

      % hack to capture the first period of the wave
      k = find ( abs(U) == max(abs(U)) );
      k = k(1);

      if k > N/2
         turn_on = 1;
      end

      min_k = min(min_k, k_old);
      if k > min_k & min_k == k_old & turn_on == 1
         break;
      end
      k_old = k; 
      
   end

   % truncate to the first period
   last_j = last_j - 1;
   Ut = Ut(1:last_j, :);

  % shift the wave by a certain amount
   shift = floor(last_j/4);
   Vt=Ut;
   Ut((last_j-shift+1):last_j, :) = Vt(1:shift, :);
   Ut(1:(last_j-shift), :)        = Vt((shift+1):last_j, :);

   num_frames = 100;
   spacing=floor(last_j/num_frames)
   
   % plot the wave
   for j=1:(last_j-spacing+1)

      U = Ut(j, :);

      if rem(j, spacing) == 1

         figure(1); clf; hold on;
         axis equal; axis off; 
         lw = 3; % linewidth
         plot(X, U, 'color', red, 'linewidth', lw);
	 
         % plot the ends of the string
         small_rad = 0.06;
         ball(0, 0, small_rad, red);
         ball(L, 0, small_rad, red);
	 
         % size of the window
         ys = 1.1;
         axis([-small_rad, L+small_rad, -ys, ys]);
      
         % small markers to keep the bounding box fixed when saving to eps
         plot(-small_rad, ys, '*', 'color', white);
         plot(L+small_rad, -ys, '*', 'color', white);

         frame_no = floor(j/spacing)+1;
         frame=sprintf('Frame%d.eps', 1000+frame_no);
         disp(frame)
         saveas(gcf, frame, 'psc2');
         
      end
   end
   
function ball(x, y, radius, color) % draw a ball of given uniform color 
   Theta=0:0.1:2*pi;
   X=radius*cos(Theta)+x;
   Y=radius*sin(Theta)+y;
   H=fill(X, Y, color);
   set(H, 'EdgeColor', color);

% The gif image was creating with the command 
% convert -antialias -loop 10000  -delay 15 -compress LZW Frame10* Movie.gif

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One-dimensional wave equation

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24 Ogos 2007

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semasa01:27, 24 Ogos 2007Gambar kenit bagi versi pada 01:27, 24 Ogos 2007274 × 121 (129 KB)Oleg Alexandrov{{Information |Description=Illustration of en:Wave equation |Source=self-made, with en:Matlab |Date=~~~~~ |Author= Oleg Alexandrov }} {{PD-self}} Category:Waves Category:Partial differential equations [[Catego

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