1、 cBL sZTsZf 1M B * sZb5 1 sZ Y tC MVb7.1 Q1.B sZf u(x1;x2;xn)(n 2)# B ux1; ux2; uxn1“ TFx1;x2;xn;u; ux1; ux2; uxn= 0 (7.1)B sZb2.BL sZF1u; ux1; ux2; uxn L BQa0(x1;x2;xn)u+nXi=1ai(x1;x2;xn) uxi= f(x1;x2;xn) (7.2)5 BL sZb3.BL Q sZ Tf(x1;x2;xn) 0a0(x1;x2;xn)u+nXi=1ai(x1;x2;xn) uxi= 0 (7.3)5 BL Q sZb4.d
2、L sZ L sZdL sZb5. EL sZdL sZ1 K L5 EL sZbc) /B EL sZnXj=1bj(x1;xn) zxj= Z(x1;x2;xn;z)12 cBL sZf ai;f;bj;Z MMXf b6. sZT bWfx1;x2;xng = B uD =l Vf u = (x1;x2;xn)Z(7.1) TFx1;x2;xn; x1; x2; xn 05u = (x1;x2;xn) sZ(7.1)B7D lbsZ+ ilB sZ(7.1)n = 2 H B T VFx;y;z; zx; zy= 0 (7.4)z = (x;y);(x;y) 2 D * bW(x;y;z
3、) w z = (x;y)Z(7.4)s w bBZ(7.1)u = (x1;x2;xn) V An + 1 bWfx1;x2;xn;ug =Bf w yN9 sZ(7.1)s wb7.2BL sZ p7.2.1 nQsl7.1cnf BsZF8:dy1dx = f1(x;y1;y2;yn);dy2dx = f2(x;y1;y2;yn);dyndx = fn(x;y1;y2;yn):(7.5)Ti , Vf (x;y1;y2;yn) PZF(7.5) uG = B d(x;y1(x);y2(x);yn(x) = 051“ T(x;y1(x);y2(x);yn(x) = c (7.6)ZF(7.
4、5)B nQsb H9ZF(7.5)B nQsb7.2BL sZ p3ZF(7.5)n nQsj(x;y1;y2;yn) = cj(j = 1;2;n) 4N TJacobi T(1;2;n)(y1;y2;yn) =flflflflflflflflflfl1y12y1 ny11y22y2 ny2 1yn2yn nynflflflflflflflflflfl(7.7)G =0b 9 VJacobi 2666641y12y1 ny11y22y2 ny2 1yn2yn nyn377775n lj(j = 1;2;n) b7.2.2sZFBL sZn = 1 fsZF|BsZdydx = f(x;y)
5、 (7.8)L ! Yy = (x;c)V(x;y) = c* Z(7.8) nQsbZ(7.8) By(x) V(x;y(x) = c d(x;y(x) = x + y dydx = 0x +yf(x;y) = 0 u = (x;y) B QL sZux +f(x;y)uy = 0 (7.9)bQ|Z(7.8) By(x) Z(7.9)u = u(x;y)1x p Vdudx =ux +uydydx =ux +f(x;y)uy = 04 cBL sZu(x;y(x) = u(x;y) = c Z(7.8) nQsb 7.1 (x;y1;y2;yn) = c ZF(7.5) nQs 1Hq G
6、 = x +f1y1 +f2y2 +fnyn = 0 (7.10) 7.2 (iB ) TA(t) nn f(t) n _ uWa t b 5 uWa t b t0# B n _ ZFx0 = A(t)x+f(t) (7.11)iB(t)l uWa t b O SHq(t0) = |5A1b 7.2 V B(x0;y01;y0n) 2 GZF(7.5) SHqyj(x0) = y0j; j = 1;2;nyj = j(x)(j = 1;2;n)i OBb(x;y1;yn) = c nQs5(x;1(x);n(x) = V7ddx(x;1(x);n(x) = 0+Yx = x0 Hx(x0;y0
7、1;y0n)+nXi=1fi(x0;y01;y0n) yi(x0;y01;y0n) = 0(x0;y01;y0n) 2 G iw T(7.10)G = b sb T(7.10)G = 1 ZF(7.5)il)9 yNddx(x;1(x);n(x) =x +f1y1 +fnynflflflflyj=j(x);j=1;2;n= 0(x;1(x);n(x) = (x;y1;yn) = c ZF(7.5) nQsb7.2BL sZ p57.2.3 nQs psZFl7.2ZF(7.5)nM nQs 8j(x;y1;yn) = cjj =1;2;nZF(7.5)Ysbs ?sZF(7.5)n nQsj(
8、x;y1;y2;yn) = cj(j =1;2;n)5YV pf ZF8:1(x;y1;y2;yn) = c12(x;y1;y2;yn) = c2n(x;y1;y2;yn) = cn(7.12)V f yjb“ZF(7.5)L p bB | T(7.12)ZF(7.5)YbN A pZF(7.5)5B p Ysbs nQsZE: n5 |ZF(7.5) / Tdxg0 =dy1g1 =dy2g2 = =dyngngj = g0fj(j = 1;2;n)b T ? pn + 1 H ,f 0;1;n P(1) 0g0 +1g1 +ngn = 0 (2) 0dx+1dy1 +ndyn f s5 =
9、 c ZB nQsb 1 pZFdxxz =dyyz =dzxyYsb 2ZFdxx =dyy =dzz +px2 +y2 +z27.2.4B QL sZ pl7.3 nXi=1Xi(x1;x2;xn) uxi= 0 (7.13)B QL sZL “ Xi(x1;x2;xn)(x(0)1 ;x(0)2 ;x(0)n ) #D V O H ,b/ / TBsZFdx1X1 =dx2X2 = =dxnXn (7.14)6 cBL sZ (7.14) sZ(7.13)+ZbsZF(7.14) cn1sZZFyN n1M nQsi(x1;x2;xn) = ci(i = 1;2;n1)b ci i b
10、V n1 nQs sZ(7.13)Yb 7.3 !i(x1;x2;xn) = ci(i = 1;2;n 1) Z(7.14)Ys5Z(7.13)Y VV Uu = “(1;2;n1) (7.15)“ M i Vf b |n5 Ti(x1;x2;xn) = ci(i = 1;2;n1) Z(7.14)Ys* f “1(x1;x2;xn);2(x1;x2;xn);n1(x1;x2;xn)= c9 ZF nQsb 8 /L !Xi(i = 1;2;n)D = H ,L !Xn 6= 0b |xn j1M Z(7.14) VV Uxj = j(xn)(j = 1;2;n 1)byi = ci(i =1
11、;2;n1) ZF(7.14) nQsyNi1(xn);2(xn);n1(xn);xn=ci;i = 1;2;n1b ci yN“1(x1;xn);n1(x1;xn)flflfl xj=j(xn)j=1;2;n1= “1(x1;xn);n1(x1;xn)= c ZF(7.14) nQsb 7.1u = “1(x1;xn);n1(x1;xn) sZ(7.13)b sZ(7.13)Y/ 1 sZ(7.13) iB Vu = “1(x1;xn);n1(x1;xn)bHqi(x1;x2;xn) = ci(i = 1;2;n1) Z(7.14) nQsyN 7.1u = i(i = 1;2;n1) Z(
12、7.13)n1bL !u = (x1;x2;xn) sZ(7.13) Bd O“ sZ(7.13)nbt sZ(7.13) V /n T8:nPi=1Xi(x1;x2;xn)(x1;x2;xn)xi= 0nPi=1Xi(x1;x2;xn)j(x1;x2;xn)xi= 0; j = 1;2;n1(7.16) / T266664x1x2 xn1x11x2 1xn n1x1n1x2 n1xn377775266664X1(x1;x2;xn)X2(x1;x2;xn)Xn(x1;x2;xn)377775= 07.2BL sZ p7Xi(i = 1;2;n)D = H ,yN ZFd ,b L M V(;1
13、;n1)(x1;x2;xn) =flflflflflflflflflflx1x2 xn1x11x2 1xn n1x1n1x2 n1xnflflflflflflflflflfl 0yNnf (x1;x2;xn);1(x1;x2;xn);n1(x1;x2;xn)M1 dM b Hq i(i = 1;n) YsM nQsyNi(i = 1;n1)9 M b“LiB Vf“ P(x1;x2;xn) = “1(x1;x2;xn);n1(x1;x2;xn)6 T“ V |f * (7.15)A 9c sZ(7.13) Ob1 7.3 # = # yN sZ(7.13)YVr T 9 b 1M sZ(7.13) p 1M f /L !B QL sZ580) 2 sZyzx xzy = 0V wL : z = x;x2 +y2 = 1s w b
