1D wave equation finite difference method [urgent]

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sing lai 2014-2-20

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https://ww2.mathworks.cn/matlabcentral/answers/116907-1d-wave-equation-finite-difference-method-urgent

评论： Aleksandra Brenko 2022-5-1

dx = .01 ; % Spacing of points on string dt =.01 ; % Size of time step

 c = 1 ;% Speed of wave propagation
 L = 1 ;% Length of string
stopTime = 30 ; % Time to run the simulation
 r = c*dt/dx ;
 n=L/dx+1
 % Set current and past to the graph of a plucked string
current = .5-.5* cos (2* pi /L * [ 0 : dx :L ] ) ;
past = current ;
for t=0: dt : stopTime
% Calculate the future position of the string
future ( 1 ) = 0 ;
 future ( 2 : n-1) = r^2*( current ( 1 : n-2)+current ( 3 : n ) ) + 2*(1-r^2)* current ( 2 : n-1) - past ( 2 : n-1);
future (n) = 0 ;
 % Set things up for the next time step
past = current ;
current = future ;
 % Plot the graph after every 10th frame
if mod( t /dt , 10) == 0
plot ( [ 0 : dx :L] , current )
axis ( [ 0 L -2 2 ] )
pause ( .001 )
end
end
 The above is the matlab code i found from internet, many questions to ask..
 1. n=L/dx + 1, what formula and meaning of this equation?
 2. current = .5-.5cos.... Is this one the initial condition?
 3. if mod(t/dt , 10) = 0, what is the meaning of this code?

Thanks everyone who willing to help me~

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Aleksandra Brenko 2022-5-1

I can't help you much but I can tell you this:

The variable x cannot be continuous for us to use a numerical method, it must be an array. The length L (observed length of the string) is divided into small sections dx. So n is the number of those sections, aka the length of the array x.
Yes, it is the position of the string at time 0
mod(t/dt , 10) = 0 means that when you divide t/dt by 10 you get a whole number and the rest is 0. So the code under if mod(t/dt , 10) = 0 will be executed whenever t/dt is divisible by 10.

Also, this code seems incomplete, eg. dx and dt are not defined.

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