9 au (x,1)x=0=N 0 (x,O)=0 (x,)x==N 非齐次边界条件,设:u(x,)=v(x)+N avaI v(X 0 v(x, t at v(x,0)=-N (x,1)=∑B,eNl nnat nZ n B=3 n丌 2N sin 5 o dcos ni5 2No nsu COS n丌 n (2k+1) (x,1)=N、4N0 (2k+1)(x)2t1(2k+1)m sIn 2k+1) 大t: (x0)=、4-7令 (m)2t 丌9. N0 N0 0 2 2 2 =   −   x u a t u 0 0 u(x,t) x= = N 0 u(x,t) x=l = N u(x,0) = 0 非齐次边界条件，设： 0 u(x,t) = v(x,t) + N 0 2 2 2 =   −   x v a t v v(x,t) x=0 = 0 v(x,t) x=l = 0 v(x,0) = −N ]sin . ( ) ( , ) exp[ 2 2 1 l n x l n a t u x t Bn n   = −  = sin . 2 0 0    d l n l N B l n  = − cos . 2 0 0 l n d n N l    = cos . 2 0 0 l l n n N    = (2 1) 4 0 + = k N . (2 1) ]sin (2 1) ( ) exp[ (2 1) 4 ( , ) 2 2 2 1 0 0 l k x l k a t k N u x t N n    + + − + = −  = 大t: ]sin . ( ) exp[ 4 ( , ) 2 2 0 0 l x l N a t u x t N    = − −