crazybird

I am solving a PDE using NDSolve. It always give a message like:

"For the method`IDA, only machine real code is available. Unable to continue with complex values or beyond floating-point exceptions."

What does this mean? My code is as following.

NDSolve[{∂_t S[z, t] == -I z S[z,t] -I A[z,t], ∂_t A[z, t] == -I S[z,t] ,
S[z, 0] == 0, S[0, t] == -I t² /2, A[z, 0] == 0, A[0, t] == t}, {S,A}, {t, 0, 1}, {z, 0, 1}, MaxSteps -> 10^{^6} ]

Any suggestions? Please Help!