Fiber Grating Using Finite Difference Method

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Fiber Grating Using Finite Difference Method

I have to solve the Fiber grating coupled-equations using FDM. These equations are coupled each other and strange inital conditions. That means ode45 from the matlab library function doesnt work here!

I am totally fresh in numerical analysis and read some books, but unlukcy, i still confuse how to do this code:(

Anyone has the program that solve this problem, pls share with me! Thank you

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The probelm is:

Parameters described:

AF(z,t) is the amplitude of forward-propagation-waves;
AB(z,t) corresponds to the backward-propagation-waves;
z and t are space and time coordinates;
AFz = dAF/dz AFt = dAF/dt;
ABz = dAF/dz ABt = dAF/dt;
i=sqrt(-1);
vg, delta, kapa, gama are constant terms.

The coupled-equations is:

i*AFz + i*AFt/vg + delta*AF + kapa*AB + gama*(|AF|^2+2*|AB|^2)*AF = 0
-i*ABz + i*ABt/vg + delta*AB + kapa*AF + gama*(|AB|^2+2*|AF|^2)*AB = 0

and the inital conditons:

AF(0,t)=A(t);
AF(z,0)=0;
AB(L,t)=0;
AB(z,0)=0

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