How do I include initial conditions in my program?

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Daisy 2013-12-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/109778-how-do-i-include-initial-conditions-in-my-program

评论： Image Analyst 2013-12-16

%Begin with global parameters, 
L = 0.64;                            %   length of string (m)
xo=L/2;                              %   mid-section of string
T = 122;                             %   tensile force of the string (N)
S=pi/(4e-6);                         %   section of the string
rho = 7.8e6;                         %   mass per unit length of string (kg/m)
c = sqrt(T/rho*S);                   %   wave velocity (m/s)
h=5;                                 %   height of string when plucked
% end global parameter
% stability condition/scheme parameters....................................................
nt=6;                                                   % number of time discretisation
t0=0;                                                   % initial time value
tf=0.3;                                                 % final time value in seconds
dt=0.005;                                               %dt=0.00025; %dt=tf/(nt-1);;                                  % time step
t = linspace(0,tf,nt);                                  %t=(t0:dt:tf);                                % time division
nx=10;                                                  % initial number of spatial discretisation with first and last nodes  
dx=L/nx;                                                % 
x=linspace(0,L,nx) ;                                    % x subdivisions on string    
x0= 0;  x(:,end)=0;                                     % boundary conditions
nx=nx-2  ;                                              % resetting number of spatial discretisation without first and last nodes 
% constructing matrices M and K...........................................
cfl=c*(dt/dx);                                          % CFL condition........STABILITY CHECKER
[M]=toeplitz([(1/c) 0 zeros(1,nx)],[(1/c) 0 zeros(1,nx)]);    
[K]=toeplitz([(-2/(dx)^2) (1/(dx)^2) 0 zeros(1,nx-1)],[(-2/(dx)^2) (1/(dx)^2) 0 zeros(1,nx-1)]);
[H]=inv(M);
% initial conditions....
U=zeros(nt,nx+2);                                        %U(space,time)
           if x<=xo
  U(:,nx) = (h*(x./xo)) %U((1:nx),1)  U(:,1)
           else  
  U(:,nx) =  (h.*((L-x)./(L-xo)))  %U(:,2)
           end

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Answer 1

Image Analyst 2013-12-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/109778-how-do-i-include-initial-conditions-in-my-program#answer_118393

You are already defining some initial values for lots of parameters. I don't know why you are asking since you seem to know how to do it.

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Daisy 2013-12-15

yes but I am not sure what the effects are. with the initial conditions the sape of the string should be visible but I am confused with what it (my decleared initial condition in the code) is meant to do, any explanation will do please.