1 ! ****************** Start Hz extended fourth-
order ********************
4 ! c11*wrrr+(
c1+c11r)*wrr + c22r*wss=fw3, (
i.e. (Lw).r=0 )
5 !
c22*wsss+(
c2+c22s)*wss + c11s*wrr=fw4, (
i.e. (Lw).
s=0 )
7 u(
i1,
i2-2*
is2,
i3,hz) = (12*fw2*dsa**2*dra**3*c11r*
c2+12*fw2*dsa**2*dra**3*c11r*c22s+12*fw2*dsa**2*dra**3*
c1*
c2+12*fw2*dsa**2*dra**3*
c1*c22s-12*fw2*dsa**2*dra**3*c11s*c22r-36*fw2*dsa**2*dra**2*c11*c22s-36*fw2*dsa**2*dra**2*c11*
c2-3*
u(i1,
i2+2*is2,i3,hz)*dra**2*c11*dsa*c22s+9*
u(i1,
i2+2*is2,i3,hz)*dra**2*c11*
c22-3*
u(i1,
i2+2*is2,i3,hz)*dra**3*c11r*
c22-3*
u(i1,
i2+2*is2,i3,hz)*dra**3*
c1*
c22+
u(i1,
i2+2*is2,i3,hz)*dra**3*c11r*dsa*
c2+
u(i1,
i2+2*is2,i3,hz)*dra**3*c11r*dsa*c22s+
u(i1,
i2+2*is2,i3,hz)*dra**3*
c1*dsa*
c2+
u(i1,
i2+2*is2,i3,hz)*dra**3*
c1*dsa*c22s-
u(i1,
i2+2*is2,i3,hz)*dra**3*c11s*dsa*c22r-3*
u(i1,
i2+2*is2,i3,hz)*dra**2*c11*dsa*
c2-48*c11s*dsa**3*c11*fw1*dra-8*c11s*dsa**3*fw3*dra**3-36*c11*
c22*dra**2*fw2*dsa-24*c11*fw4*dsa**3*dra**2+12*dra**3*c11r*
c22*fw2*dsa+12*dra**3*
c1*
c22*fw2*dsa+8*dra**3*c11r*fw4*dsa**3+8*dra**3*
c1*fw4*dsa**3-48*c11*dsa*dra**2*
c2*
u(i1,
i2,i3,hz)-48*c11*dsa*dra**2*c22s*
u(i1,i2,i3,hz)+16*dra**3*c11r*dsa*
c2*
u(i1,i2,i3,hz)+16*dra**3*c11r*dsa*c22s*
u(i1,i2,i3,hz)+16*dra**3*
c1*dsa*c22s*
u(i1,i2,i3,hz)+16*dra**3*
c1*dsa*
c2*
u(i1,i2,i3,hz)-16*c11s*dsa*c22r*dra**3*
u(i1,i2,i3,hz)-48*c11*c11s*dsa**3*
u(i1,i2,i3,hz)+48*c11s*dsa**3*c11*
u(i1+is1,i2,i3,hz)-16*dra**3*
c1*dsa*
c2*
u(i1,i2+is2,i3,hz)+16*c11s*dsa*c22r*dra**3*
u(i1,i2+is2,i3,hz)-16*dra**3*
c1*dsa*c22s*
u(i1,i2+is2,i3,hz)-16*dra**3*c11r*dsa*
c2*
u(i1,i2+is2,i3,hz)-16*dra**3*c11r*dsa*c22s*
u(i1,i2+is2,i3,hz)+48*c11*dsa*dra**2*
c2*
u(i1,i2+is2,i3,hz)+48*c11*dsa*dra**2*c22s*
u(i1,i2+is2,i3,hz))/dra**2/(-3*c11*dsa*c22s-3*c11*dsa*
c2+dra*c11r*dsa*
c2+dra*c11r*dsa*c22s+9*c11*
c22-3*dra*c11r*
c22+dra*
c1*dsa*
c2+dra*
c1*dsa*c22s-c11s*dsa*c22r*dra-3*dra*
c1*
c22)
9 u(i1-is1,i2,i3,hz) = -1/dsa**2*(6*dsa**2*
u(i1,i2,i3,hz)*dra*
c1*
c22-2*dsa**3*
u(i1,i2,i3,hz)*dra*c11r*
c2-2*dsa**3*
u(i1,i2,i3,hz)*dra*c11r*c22s+2*c11s*dsa**3*
u(i1,i2,i3,hz)*c22r*dra+6*dsa**2*
u(i1,i2,i3,hz)*dra*c11r*
c22-2*dsa**3*
u(i1,i2,i3,hz)*dra*
c1*
c2-2*dsa**3*
u(i1,i2,i3,hz)*dra*
c1*c22s+6*
c22*c22r*dra**3*
u(i1,i2,i3,hz)+3*dsa**3*c22s*c11*
u(i1+is1,i2,i3,hz)-3*dsa**2*
u(i1+is1,i2,i3,hz)*dra*c11r*
c22-3*dsa**2*
u(i1+is1,i2,i3,hz)*dra*
c1*
c22-9*
c22*dsa**2*c11*
u(i1+is1,i2,i3,hz)+dsa**3*
u(i1+is1,i2,i3,hz)*dra*c11r*c22s-c11s*dsa**3*
u(i1+is1,i2,i3,hz)*c22r*dra+dsa**3*
u(i1+is1,i2,i3,hz)*dra*
c1*
c2+dsa**3*
u(i1+is1,i2,i3,hz)*dra*
c1*c22s+dsa**3*
u(i1+is1,i2,i3,hz)*dra*c11r*
c2+3*
c2*dsa**3*c11*
u(i1+is1,i2,i3,hz)-6*
c22*c22r*dra**3*
u(i1,i2+is2,i3,hz)-dsa**3*c22s*fw3*dra**3+18*
c22*dsa**2*c11*fw1*dra+3*
c22*dsa**2*fw3*dra**3-6*dsa**3*c22s*c11*fw1*dra+fw4*dsa**3*dra**3*c22r-6*
c2*dsa**3*c11*fw1*dra-
c2*dsa**3*fw3*dra**3+6*
c22*dra**3*fw2*dsa*c22r)/(-3*c11*dsa*c22s-3*c11*dsa*
c2+dra*c11r*dsa*
c2+dra*c11r*dsa*c22s+9*c11*
c22-3*dra*c11r*
c22+dra*
c1*dsa*
c2+dra*
c1*dsa*c22s-c11s*dsa*c22r*dra-3*dra*
c1*
c22)
11 u(i1,i2-is2,i3,hz) = -(6*c11*c11s*dsa**3*
u(i1,i2,i3,hz)-2*dra**3*
c1*dsa*c22s*
u(i1,i2,i3,hz)-2*dra**3*
c1*dsa*
c2*
u(i1,i2,i3,hz)+2*c11s*dsa*c22r*dra**3*
u(i1,i2,i3,hz)-2*dra**3*c11r*dsa*c22s*
u(i1,i2,i3,hz)+6*c11*dsa*dra**2*
c2*
u(i1,i2,i3,hz)+6*c11*dsa*dra**2*c22s*
u(i1,i2,i3,hz)-2*dra**3*c11r*dsa*
c2*
u(i1,i2,i3,hz)-6*c11s*dsa**3*c11*
u(i1+is1,i2,i3,hz)-c11s*dsa*c22r*dra**3*
u(i1,i2+is2,i3,hz)+dra**3*
c1*dsa*c22s*
u(i1,i2+is2,i3,hz)+dra**3*c11r*dsa*
c2*
u(i1,i2+is2,i3,hz)+dra**3*c11r*dsa*c22s*
u(i1,i2+is2,i3,hz)+dra**3*
c1*dsa*
c2*
u(i1,i2+is2,i3,hz)-3*c11*dsa*dra**2*
c2*
u(i1,i2+is2,i3,hz)-3*c11*dsa*dra**2*c22s*
u(i1,i2+is2,i3,hz)+3*dra**3*c11r*
c22*
u(i1,i2+is2,i3,hz)-9*c11*
c22*dra**2*
u(i1,i2+is2,i3,hz)+3*dra**3*
c1*
c22*
u(i1,i2+is2,i3,hz)+6*c11s*dsa**3*c11*fw1*dra+c11s*dsa**3*fw3*dra**3+18*c11*
c22*dra**2*fw2*dsa+3*c11*fw4*dsa**3*dra**2-6*dra**3*c11r*
c22*fw2*dsa-6*dra**3*
c1*
c22*fw2*dsa-dra**3*c11r*fw4*dsa**3-dra**3*
c1*fw4*dsa**3)/dra**2/(-3*c11*dsa*c22s-3*c11*dsa*
c2+dra*c11r*dsa*
c2+dra*c11r*dsa*c22s+9*c11*
c22-3*dra*c11r*
c22+dra*
c1*dsa*
c2+dra*
c1*dsa*c22s-c11s*dsa*c22r*dra-3*dra*
c1*
c22)
13 u(i1-2*is1,i2,i3,hz) = (-36*fw1*dra**2*dsa**2*c11r*
c22+12*fw1*dra**2*dsa**3*
c1*
c2+12*fw1*dra**2*dsa**3*
c1*c22s-12*fw1*dra**2*dsa**3*c11s*c22r-36*fw1*dra**2*dsa**2*
c1*
c22+12*fw1*dra**2*dsa**3*c11r*
c2+12*fw1*dra**2*dsa**3*c11r*c22s+48*dsa**2*
u(i1+is1,i2,i3,hz)*dra*c11r*
c22+48*dsa**2*
u(i1+is1,i2,i3,hz)*dra*
c1*
c22-48*
c22*c22r*dra**3*
u(i1,i2,i3,hz)+16*dsa**3*
u(i1,i2,i3,hz)*dra*
c1*c22s-16*c11s*dsa**3*
u(i1,i2,i3,hz)*c22r*dra-48*dsa**2*
u(i1,i2,i3,hz)*dra*
c1*
c22+16*dsa**3*
u(i1,i2,i3,hz)*dra*c11r*
c2+16*dsa**3*
u(i1,i2,i3,hz)*dra*c11r*c22s-48*dsa**2*
u(i1,i2,i3,hz)*dra*c11r*
c22+16*dsa**3*
u(i1,i2,i3,hz)*dra*
c1*
c2-16*dsa**3*
u(i1+is1,i2,i3,hz)*dra*
c1*
c2-16*dsa**3*
u(i1+is1,i2,i3,hz)*dra*
c1*c22s-16*dsa**3*
u(i1+is1,i2,i3,hz)*dra*c11r*
c2-16*dsa**3*
u(i1+is1,i2,i3,hz)*dra*c11r*c22s+16*c11s*dsa**3*
u(i1+is1,i2,i3,hz)*c22r*dra+48*
c22*c22r*dra**3*
u(i1,i2+is2,i3,hz)+
u(i1+2*is1,i2,i3,hz)*dsa**3*dra*c11r*
c2-3*
u(i1+2*is1,i2,i3,hz)*dsa**2*dra*
c1*
c22+
u(i1+2*is1,i2,i3,hz)*dsa**3*dra*c11r*c22s-3*
u(i1+2*is1,i2,i3,hz)*dsa**2*dra*c11r*
c22+
u(i1+2*is1,i2,i3,hz)*dsa**3*dra*
c1*
c2+
u(i1+2*is1,i2,i3,hz)*dsa**3*dra*
c1*c22s-
u(i1+2*is1,i2,i3,hz)*dsa**3*c11s*c22r*dra-3*
u(i1+2*is1,i2,i3,hz)*dsa**3*c11*
c2+9*
u(i1+2*is1,i2,i3,hz)*dsa**2*c11*
c22-3*
u(i1+2*is1,i2,i3,hz)*dsa**3*c11*c22s+8*dsa**3*c22s*fw3*dra**3-36*
c22*dsa**2*c11*fw1*dra-24*
c22*dsa**2*fw3*dra**3+12*dsa**3*c22s*c11*fw1*dra-8*fw4*dsa**3*dra**3*c22r+12*
c2*dsa**3*c11*fw1*dra+8*
c2*dsa**3*fw3*dra**3-48*
c22*dra**3*fw2*dsa*c22r)/dsa**2/(-3*c11*dsa*c22s-3*c11*dsa*
c2+dra*c11r*dsa*
c2+dra*c11r*dsa*c22s+9*c11*
c22-3*dra*c11r*
c22+dra*
c1*dsa*
c2+dra*
c1*dsa*c22s-c11s*dsa*c22r*dra-3*dra*
c1*
c22)
17 ! ****************** done Hz extended fourth-
order ********************
