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*刘德朋(杭州电子工业学院理学分院杭州310018),.,w(x,t),.,w(x,t),,w(x,t).O175.21,,().,.w(x,t)[1],.w(x,t),w(x,t),,w(x,t),,w(x,t),.(1)ut=a2uxx+f(x,t)(0x1,t0)(1)mux(0,t)-nu(0,t)=K(t)[2](t\0)(2)pux(l,t)+qu(l,t)=L(t)[2](t\0)(3)u(x,0)=U(x)(0[x[l)f(x,t)U(x)K(t)L(t),mn\0,pq\0,,p+qX0(2)(3):m=p=0nqX0(4)n=q=0mpX0(5)mnpqX0(6),m=q=0npX0(7)m=0npqX0(8)p=0mnqX0(9)q=0mnpX0(10)n=p=0mqX0(11)n=0mpqX0(12)12(,)1331322123.(1)(2)(3),w(x,t):u(x,t)=v(x,t)52STUDIESINCOLLEGEMATHEMATICSVo.l9,No.3May,2006*:2003-12-23,:2004-03-28+w(x,t),v(x,t),,.w(x,t)u(x,t)[3].2(2)(3),t,:mux(0,t)-nu(0,t)=K(13)pux(l,t)+qu(l,t)=L(14)K,L.w(x,t),w(x),x,:u(x,t)=v(x,t)+w(x)(15)(15)(1)(13)(14),:1a2[vt-a2vxx-f(x,t)]=wd(x)(16)[mvx(0,t)-nv(0,t)]+[mwc(0)-nw(0)]=K(17)[pvx(l,t)+q(l,t)]+[pwc(l)+qw(l)]=L(18)w(x)u(x,t),mwc(0)-nw(0)=K(19)pwc(l)+qw(l)=L(20)v(x,t).(16),,k,wd(x)=k(21)211k=0,w(x)=Ax+B(22)(19)(20)(22),AB,w(x)=qK+nLmq+np+nql(x+mn)-Kn(23),(23)(4)(6)(7)(8)(9)(10).212kX0,:w(x)=k2x2+cx+D(24)(5)(11)(12)w(x),D=0,(19)(20)(24)kc,:w(x)=mL-pK-Kqlml(2p+ql)x2+Kmx(25),(25)(5)(11)(12)w(x).213211212w(x):w(x)=qK+nLmq+np+nql(x+mn)-Kn(nX0)mu-pK-Kqlml(2p+ql)x2+Kmx(mX0)(26)5393:3,t,K(t)L(t),(26)KLK(t)L(t),w(x,t)=qK(t)+nL(t)mq+np+nql(x+mn)-K(t)m(nX0)mL(t)-pK(t)-qlK(t)ml(2p+ql)x2+K(t)mx(mX0)(27),(27).4utt=a2uxx+f(x,t)(0xl,t0(28)mux(0,t)-nu(0,t)=K(t)(t\0)(2)pux(l,t)+qu(l,t)=L(t)(t\0)(3)u(x,0)=U(x),ut(x,0)=W(x)(0[x[l),K(t)=K,L(t)=L,(K,L),w(x#t)=w(x),(15)(28),1a2[Vtt-a2Vxx-f(x#t)]=Wd(x)(29)(29)(16),.(26)(27)(Ò).(27)(26),(27)w(x,t).[1].[M].:,1989.285-288.[2].[M].:,1985-16.[3].[M].:,1976-33.(上接第40页),f(x)-p(x)=f(4)(N)4!P(x)[M4!P(x),P(x)=(x-2)(x-4)(x-6)(x-8).,|P(x)|.,.Pc(x)=(x-4)(x-6)(x-8)+(x-2)(x-6)(x-8)+(x-2)(x-4)(x-8)+(x-2)(x-4)(x-6)=0,,,,,.2,4,6,85,t=x-5,:x=t+5P(x)=P(t+5)=(t+3)(t+1)(t-1)(t-3)=(t2-9)(t2-1)Pc(t+5)=2t(t2-1)+2t(t2-9)=4t(t2-5),:Pc(t+5)=0,:t=0,t=?5,x=5,x=5?5,P(5)=9,P(5?5)=-16.P(2)=P(8)=0,:|f(x)-p(x)|[M4!#16=23M5420065