Fiber Grating Using Finite Difference Method

  1. 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

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     
  2. jcsd
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