REALISTIC AND NON-REALISTIC STRINGS

## A 'realistic', 'non-elastic' string, which responses to any
## bending and has stifness. This script takes in the previous
## and the present profiles and iterates to find
## the profile in the next time step. The ratio 'r' is not 1
## like in the 'non-realistic' string since the speed of the wave
## always less than the speed of the string it should be less than 1
## for best and most stable solution
##constants
dx=1e-2 ## Spatial increment (m)
L=2 ## Length of the string (m)
M=L/dx ## Dimensionless partition
E=1e-4 ## Dimensionless stiffnes
function ynext=propagate_stiff(ynow,yprev,r)
## Quick and dirty way to fix boundary conditions -- for each step
## they are the same as the previous step.
ynext=ynow;
ynow(1)=ynow(2)=0;
##Entering the loop
for i=3:length(ynow)-1
## boundary condition
ynow(length(ynow)-1)=ynow(length(ynow)-2)=0;
## Divide the ynext with many terms into three parts for easiness
ynext(i)=(2−(2*r^2)−(6*E*(r^2)*(M^2)))*ynow(i)−yprev(i);
ynext(i)=ynext(i)+(r^2)*(1+4*E*(M^2))*(ynow(i+1)+ynow(i−1));
ynext(i)=ynext(i)-E*(r^2)*(M^2)*(ynow(i+2)+ynow(i−2));
endfor
endfunction