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movmod.f90
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movmod.f90
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MODULE movmod
CONTAINS
SUBROUTINE shape_function(phi,j,k,s)
! Returns the Hermite interpolating polynomials on [0,1] and their
! derivatives up to order 6
IMPLICIT NONE
INTEGER, INTENT(IN) :: j, k
REAL(kind=8), INTENT(IN) :: s
REAL(kind=8), INTENT(OUT) :: phi
if (j == 0) then
if (k == 0) then
phi = (1.0d0) - &
(462.0d0)*(s**6.0d0) + &
(1980.0d0)*(s**7.0d0) - &
(3465.0d0)*(s**8.0d0) + &
(3080.0d0)*(s**9.0d0) - &
(1386.0d0)*(s**10.0d0) + &
(252.0d0)*(s**11.0d0)
else if (k == 1) then
phi = -(2772.0d0)*(s**5.0d0) + &
(13860.0d0)*(s**6.0d0) - &
(27720.0d0)*(s**7.0d0) + &
(27720.0d0)*(s**8.0d0) - &
(13860.0d0)*(s**9.0d0) + &
(2772.0d0)*(s**10.0d0)
else if (k == 2) then
phi = -(13860.0d0)*(s**4.0d0) + &
(83160.0d0)*(s**5.0d0) - &
(194040.0d0)*(s**6.0d0) + &
(221760.0d0)*(s**7.0d0) - &
(124740.0d0)*(s**8.0d0) + &
(27720.0d0)*(s**9.0d0)
else if (k == 3) then
phi = -(55440.0d0)*(s**3.0d0) + &
(415800.0d0)*(s**4.0d0) - &
(1164240.0d0)*(s**5.0d0) + &
(1552320.0d0)*(s**6.0d0) - &
(997920.0d0)*(s**7.0d0) + &
(249480.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(166320.0d0)*(s**2.0d0) + &
(1663200.0d0)*(s**3.0d0) - &
(5821200.0d0)*(s**4.0d0) + &
(9313920.0d0)*(s**5.0d0) - &
(6985440.0d0)*(s**6.0d0) + &
(1995840.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(332640.0d0)*s + &
(4989600.0d0)*(s**2.0d0) - &
(23284800.0d0)*(s**3.0d0) + &
(46569600.0d0)*(s**4.0d0) - &
(41912640.0d0)*(s**5.0d0) + &
(13970880.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(332640.0d0) + &
(9979200.0d0)*s - &
(69854400.0d0)*(s**2.0d0) + &
(186278400.0d0)*(s**3.0d0) - &
(209563200.0d0)*(s**4.0d0) + &
(83825280.0d0)*(s**5.0d0)
end if
else if (j == 1) then
if (k == 0) then
phi = s - &
(252.0d0)*(s**6.0d0) + &
(1050.0d0)*(s**7.0d0) - &
(1800.0d0)*(s**8.0d0) + &
(1575.0d0)*(s**9.0d0) - &
(700.0d0)*(s**10.0d0) + &
(126.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (1.0d0) - &
(1512.0d0)*(s**5.0d0) + &
(7350.0d0)*(s**6.0d0) - &
(14400.0d0)*(s**7.0d0) + &
(14175.0d0)*(s**8.0d0) - &
(7000.0d0)*(s**9.0d0) + &
(1386.0d0)*(s**10.0d0)
else if (k == 2) then
phi = -(7560.0d0)*(s**4.0d0) + &
(44100.0d0)*(s**5.0d0) - &
(100800.0d0)*(s**6.0d0) + &
(113400.0d0)*(s**7.0d0) - &
(63000.0d0)*(s**8.0d0) + &
(13860.0d0)*(s**9.0d0)
else if (k == 3) then
phi = -(30240.0d0)*(s**3.0d0) + &
(220500.0d0)*(s**4.0d0) - &
(604800.0d0)*(s**5.0d0) + &
(793800.0d0)*(s**6.0d0) - &
(504000.0d0)*(s**7.0d0) + &
(124740.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(90720.0d0)*(s**2.0d0) + &
(882000.0d0)*(s**3.0d0) - &
(3024000.0d0)*(s**4.0d0) + &
(4762800.0d0)*(s**5.0d0) - &
(3528000.0d0)*(s**6.0d0) + &
(997920.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(181440.0d0)*s + &
(2646000.0d0)*(s**2.0d0) - &
(12096000.0d0)*(s**3.0d0) + &
(23814000.0d0)*(s**4.0d0) - &
(21168000.0d0)*(s**5.0d0) + &
(6985440.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(181440.0d0) + &
(5292000.0d0)*s - &
(36288000.0d0)*(s**2.0d0) + &
(95256000.0d0)*(s**3.0d0) - &
(105840000.0d0)*(s**4.0d0) + &
(41912640.0d0)*(s**5.0d0)
end if
else if (j == 2) then
if (k == 0) then
phi = (1.0d0/2.0d0)*(s**2.0d0) - &
(63.0d0)*(s**6.0d0) + &
(252.0d0)*(s**7.0d0) - &
(420.0d0)*(s**8.0d0) + &
(360.0d0)*(s**9.0d0) - &
(315.0d0/2.0d0)*(s**10.0d0) + &
(28.0d0)*(s**11.0d0)
else if (k == 1) then
phi = s - &
(378.0d0)*(s**5.0d0) + &
(1764.0d0)*(s**6.0d0) - &
(3360.0d0)*(s**7.0d0) + &
(3240.0d0)*(s**8.0d0) - &
(1575.0d0)*(s**9.0d0) + &
(308.0d0)*(s**10.0d0)
else if (k == 2) then
phi = (1.0d0) - &
(1890.0d0)*(s**4.0d0) + &
(10584.0d0)*(s**5.0d0) - &
(23520.0d0)*(s**6.0d0) + &
(25920.0d0)*(s**7.0d0) - &
(14175.0d0)*(s**8.0d0) + &
(3080.0d0)*(s**9.0d0)
else if (k == 3) then
phi = -(7560.0d0)*(s**3.0d0) + &
(52920.0d0)*(s**4.0d0) - &
(141120.0d0)*(s**5.0d0) + &
(181440.0d0)*(s**6.0d0) - &
(113400.0d0)*(s**7.0d0) + &
(27720.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(22680.0d0)*(s**2.0d0) + &
(211680.0d0)*(s**3.0d0) - &
(705600.0d0)*(s**4.0d0) + &
(1088640.0d0)*(s**5.0d0) - &
(793800.0d0)*(s**6.0d0) + &
(221760.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(45360.0d0)*s + &
(635040.0d0)*(s**2.0d0) - &
(2822400.0d0)*(s**3.0d0) + &
(5443200.0d0)*(s**4.0d0) - &
(4762800.0d0)*(s**5.0d0) + &
(1552320.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(45360.0d0) + &
(1270080.0d0)*s - &
(8467200.0d0)*(s**2.0d0) + &
(21772800.0d0)*(s**3.0d0) - &
(23814000.0d0)*(s**4.0d0) + &
(9313920.0d0)*(s**5.0d0)
end if
else if (j == 3) then
if (k == 0) then
phi = (1.0d0/6.0d0)*(s**3.0d0) - &
(28.0d0/3.0d0)*(s**6.0d0) + &
(35.0d0)*(s**7.0d0) - &
(56.0d0)*(s**8.0d0) + &
(140.0d0/3.0d0)*(s**9.0d0) - &
(20.0d0)*(s**10.0d0) + &
(7.0d0/2.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (1.0d0/2.0d0)*(s**2.0d0) - &
(56.0d0)*(s**5.0d0) + &
(245.0d0)*(s**6.0d0) - &
(448.0d0)*(s**7.0d0) + &
(420.0d0)*(s**8.0d0) - &
(200.0d0)*(s**9.0d0) + &
(77.0d0/2.0d0)*(s**10.0d0)
else if (k == 2) then
phi = s - &
(280.0d0)*(s**4.0d0) + &
(1470.0d0)*(s**5.0d0) - &
(3136.0d0)*(s**6.0d0) + &
(3360.0d0)*(s**7.0d0) - &
(1800.0d0)*(s**8.0d0) + &
(385.0d0)*(s**9.0d0)
else if (k == 3) then
phi = (1.0d0) - &
(1120.0d0)*(s**3.0d0) + &
(7350.0d0)*(s**4.0d0) - &
(18816.0d0)*(s**5.0d0) + &
(23520.0d0)*(s**6.0d0) - &
(14400.0d0)*(s**7.0d0) + &
(3465.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(3360.0d0)*(s**2.0d0) + &
(29400.0d0)*(s**3.0d0) - &
(94080.0d0)*(s**4.0d0) + &
(141120.0d0)*(s**5.0d0) - &
(100800.0d0)*(s**6.0d0) + &
(27720.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(6720.0d0)*s + &
(88200.0d0)*(s**2.0d0) - &
(376320.0d0)*(s**3.0d0) + &
(705600.0d0)*(s**4.0d0) - &
(604800.0d0)*(s**5.0d0) + &
(194040.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(6720.0d0) + &
(176400.0d0)*s - &
(1128960.0d0)*(s**2.0d0) + &
(2822400.0d0)*(s**3.0d0) - &
(3024000.0d0)*(s**4.0d0) + &
(1164240.0d0)*(s**5.0d0)
end if
else if (j == 4) then
if (k == 0) then
phi = (1.0d0/24.0d0)*(s**4.0d0) - &
(7.0d0/8.0d0)*(s**6.0d0) + &
(35.0d0/12.0d0)*(s**7.0d0) - &
(35.0d0/8.0d0)*(s**8.0d0) + &
(7.0d0/2.0d0)*(s**9.0d0) - &
(35.0d0/24.0d0)*(s**10.0d0) + &
(1.0d0/4.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (1.0d0/6.0d0)*(s**3.0d0) - &
(21.0d0/4.0d0)*(s**5.0d0) + &
(245.0d0/12.0d0)*(s**6.0d0) - &
(35.0d0)*(s**7.0d0) + &
(63.0d0/2.0d0)*(s**8.0d0) - &
(175.0d0/12.0d0)*(s**9.0d0) + &
(11.0d0/4.0d0)*(s**10.0d0)
else if (k == 2) then
phi = (1.0d0/2.0d0)*(s**2.0d0) - &
(105.0d0/4.0d0)*(s**4.0d0) + &
(245.0d0/2.0d0)*(s**5.0d0) - &
(245.0d0)*(s**6.0d0) + &
(252.0d0)*(s**7.0d0) - &
(525.0d0/4.0d0)*(s**8.0d0) + &
(55.0d0/2.0d0)*(s**9.0d0)
else if (k == 3) then
phi = s - &
(105.0d0)*(s**3.0d0) + &
(1225.0d0/2.0d0)*(s**4.0d0) - &
(1470.0d0)*(s**5.0d0) + &
(1764.0d0)*(s**6.0d0) - &
(1050.0d0)*(s**7.0d0) + &
(495.0d0/2.0d0)*(s**8.0d0)
else if (k == 4) then
phi = (1.0d0) - &
(315.0d0)*(s**2.0d0) + &
(2450.0d0)*(s**3.0d0) - &
(7350.0d0)*(s**4.0d0) + &
(10584.0d0)*(s**5.0d0) - &
(7350.0d0)*(s**6.0d0) + &
(1980.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(630.0d0)*s + &
(7350.0d0)*(s**2.0d0) - &
(29400.0d0)*(s**3.0d0) + &
(52920.0d0)*(s**4.0d0) - &
(44100.0d0)*(s**5.0d0) + &
(13860.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(630.0d0) + &
(14700.0d0)*s - &
(88200.0d0)*(s**2.0d0) + &
(211680.0d0)*(s**3.0d0) - &
(220500.0d0)*(s**4.0d0) + &
(83160.0d0)*(s**5.0d0)
end if
else if (j == 5) then
if (k == 0) then
phi = (1.0d0/120.0d0)*(s**5.0d0) - &
(1.0d0/20.0d0)*(s**6.0d0) + &
(1.0d0/8.0d0)*(s**7.0d0) - &
(1.0d0/6.0d0)*(s**8.0d0) + &
(1.0d0/8.0d0)*(s**9.0d0) - &
(1.0d0/20.0d0)*(s**10.0d0) + &
(1.0d0/120.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (1.0d0/24.0d0)*(s**4.0d0) - &
(3.0d0/10.0d0)*(s**5.0d0) + &
(7.0d0/8.0d0)*(s**6.0d0) - &
(4.0d0/3.0d0)*(s**7.0d0) + &
(9.0d0/8.0d0)*(s**8.0d0) - &
(1.0d0/2.0d0)*(s**9.0d0) + &
(11.0d0/120.0d0)*(s**10.0d0)
else if (k == 2) then
phi = (1.0d0/6.0d0)*(s**3.0d0) - &
(3.0d0/2.0d0)*(s**4.0d0) + &
(21.0d0/4.0d0)*(s**5.0d0) - &
(28.0d0/3.0d0)*(s**6.0d0) + &
(9.0d0)*(s**7.0d0) - &
(9.0d0/2.0d0)*(s**8.0d0) + &
(11.0d0/12.0d0)*(s**9.0d0)
else if (k == 3) then
phi = (1.0d0/2.0d0)*(s**2.0d0) - &
(6.0d0)*(s**3.0d0) + &
(105.0d0/4.0d0)*(s**4.0d0) - &
(56.0d0)*(s**5.0d0) + &
(63.0d0)*(s**6.0d0) - &
(36.0d0)*(s**7.0d0) + &
(33.0d0/4.0d0)*(s**8.0d0)
else if (k == 4) then
phi = s - &
(18.0d0)*(s**2.0d0) + &
(105.0d0)*(s**3.0d0) - &
(280.0d0)*(s**4.0d0) + &
(378.0d0)*(s**5.0d0) - &
(252.0d0)*(s**6.0d0) + &
(66.0d0)*(s**7.0d0)
else if (k == 5) then
phi = (1.0d0) - &
(36.0d0)*s + &
(315.0d0)*(s**2.0d0) - &
(1120.0d0)*(s**3.0d0) + &
(1890.0d0)*(s**4.0d0) - &
(1512.0d0)*(s**5.0d0) + &
(462.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(36.0d0) + &
(630.0d0)*s - &
(3360.0d0)*(s**2.0d0) + &
(7560.0d0)*(s**3.0d0) - &
(7560.0d0)*(s**4.0d0) + &
(2772.0d0)*(s**5.0d0)
end if
else if (j == 6) then
if (k == 0) then
phi = (462.0d0)*(s**6.0d0) - &
(1980.0d0)*(s**7.0d0) + &
(3465.0d0)*(s**8.0d0) - &
(3080.0d0)*(s**9.0d0) + &
(1386.0d0)*(s**10.0d0) - &
(252.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (2772.0d0)*(s**5.0d0) - &
(13860.0d0)*(s**6.0d0) + &
(27720.0d0)*(s**7.0d0) - &
(27720.0d0)*(s**8.0d0) + &
(13860.0d0)*(s**9.0d0) - &
(2772.0d0)*(s**10.0d0)
else if (k == 2) then
phi = (13860.0d0)*(s**4.0d0) - &
(83160.0d0)*(s**5.0d0) + &
(194040.0d0)*(s**6.0d0) - &
(221760.0d0)*(s**7.0d0) + &
(124740.0d0)*(s**8.0d0) - &
(27720.0d0)*(s**9.0d0)
else if (k == 3) then
phi = (55440.0d0)*(s**3.0d0) - &
(415800.0d0)*(s**4.0d0) + &
(1164240.0d0)*(s**5.0d0) - &
(1552320.0d0)*(s**6.0d0) + &
(997920.0d0)*(s**7.0d0) - &
(249480.0d0)*(s**8.0d0)
else if (k == 4) then
phi = (166320.0d0)*(s**2.0d0) - &
(1663200.0d0)*(s**3.0d0) + &
(5821200.0d0)*(s**4.0d0) - &
(9313920.0d0)*(s**5.0d0) + &
(6985440.0d0)*(s**6.0d0) - &
(1995840.0d0)*(s**7.0d0)
else if (k == 5) then
phi = (332640.0d0)*s - &
(4989600.0d0)*(s**2.0d0) + &
(23284800.0d0)*(s**3.0d0) - &
(46569600.0d0)*(s**4.0d0) + &
(41912640.0d0)*(s**5.0d0) - &
(13970880.0d0)*(s**6.0d0)
else if (k == 6) then
phi = (332640.0d0) - &
(9979200.0d0)*s + &
(69854400.0d0)*(s**2.0d0) - &
(186278400.0d0)*(s**3.0d0) + &
(209563200.0d0)*(s**4.0d0) - &
(83825280.0d0)*(s**5.0d0)
end if
else if (j == 7) then
if (k == 0) then
phi = -(210.0d0)*(s**6.0d0) + &
(930.0d0)*(s**7.0d0) - &
(1665.0d0)*(s**8.0d0) + &
(1505.0d0)*(s**9.0d0) - &
(686.0d0)*(s**10.0d0) + &
(126.0d0)*(s**11.0d0)
else if (k == 1) then
phi = -(1260.0d0)*(s**5.0d0) + &
(6510.0d0)*(s**6.0d0) - &
(13320.0d0)*(s**7.0d0) + &
(13545.0d0)*(s**8.0d0) - &
(6860.0d0)*(s**9.0d0) + &
(1386.0d0)*(s**10.0d0)
else if (k == 2) then
phi = -(6300.0d0)*(s**4.0d0) + &
(39060.0d0)*(s**5.0d0) - &
(93240.0d0)*(s**6.0d0) + &
(108360.0d0)*(s**7.0d0) - &
(61740.0d0)*(s**8.0d0) + &
(13860.0d0)*(s**9.0d0)
else if (k == 3) then
phi = -(25200.0d0)*(s**3.0d0) + &
(195300.0d0)*(s**4.0d0) - &
(559440.0d0)*(s**5.0d0) + &
(758520.0d0)*(s**6.0d0) - &
(493920.0d0)*(s**7.0d0) + &
(124740.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(75600.0d0)*(s**2.0d0) + &
(781200.0d0)*(s**3.0d0) - &
(2797200.0d0)*(s**4.0d0) + &
(4551120.0d0)*(s**5.0d0) - &
(3457440.0d0)*(s**6.0d0) + &
(997920.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(151200.0d0)*s + &
(2343600.0d0)*(s**2.0d0) - &
(11188800.0d0)*(s**3.0d0) + &
(22755600.0d0)*(s**4.0d0) - &
(20744640.0d0)*(s**5.0d0) + &
(6985440.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(151200.0d0) + &
(4687200.0d0)*s - &
(33566400.0d0)*(s**2.0d0) + &
(91022400.0d0)*(s**3.0d0) - &
(103723200.0d0)*(s**4.0d0) + &
(41912640.0d0)*(s**5.0d0)
end if
else if (j == 8) then
if (k == 0) then
phi = (42.0d0)*(s**6.0d0) - &
(192.0d0)*(s**7.0d0) + &
(705.0d0/2.0d0)*(s**8.0d0) - &
(325.0d0)*(s**9.0d0) + &
(301.0d0/2.0d0)*(s**10.0d0) - &
(28.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (252.0d0)*(s**5.0d0) - &
(1344.0d0)*(s**6.0d0) + &
(2820.0d0)*(s**7.0d0) - &
(2925.0d0)*(s**8.0d0) + &
(1505.0d0)*(s**9.0d0) - &
(308.0d0)*(s**10.0d0)
else if (k == 2) then
phi = (1260.0d0)*(s**4.0d0) - &
(8064.0d0)*(s**5.0d0) + &
(19740.0d0)*(s**6.0d0) - &
(23400.0d0)*(s**7.0d0) + &
(13545.0d0)*(s**8.0d0) - &
(3080.0d0)*(s**9.0d0)
else if (k == 3) then
phi = (5040.0d0)*(s**3.0d0) - &
(40320.0d0)*(s**4.0d0) + &
(118440.0d0)*(s**5.0d0) - &
(163800.0d0)*(s**6.0d0) + &
(108360.0d0)*(s**7.0d0) - &
(27720.0d0)*(s**8.0d0)
else if (k == 4) then
phi = (15120.0d0)*(s**2.0d0) - &
(161280.0d0)*(s**3.0d0) + &
(592200.0d0)*(s**4.0d0) - &
(982800.0d0)*(s**5.0d0) + &
(758520.0d0)*(s**6.0d0) - &
(221760.0d0)*(s**7.0d0)
else if (k == 5) then
phi = (30240.0d0)*s - &
(483840.0d0)*(s**2.0d0) + &
(2368800.0d0)*(s**3.0d0) - &
(4914000.0d0)*(s**4.0d0) + &
(4551120.0d0)*(s**5.0d0) - &
(1552320.0d0)*(s**6.0d0)
else if (k == 6) then
phi = (30240.0d0) - &
(967680.0d0)*s + &
(7106400.0d0)*(s**2.0d0) - &
(19656000.0d0)*(s**3.0d0) + &
(22755600.0d0)*(s**4.0d0) - &
(9313920.0d0)*(s**5.0d0)
end if
else if (j == 9) then
if (k == 0) then
phi = -(14.0d0/3.0d0)*(s**6.0d0) + &
(22.0d0)*(s**7.0d0) - &
(83.0d0/2.0d0)*(s**8.0d0) + &
(235.0d0/6.0d0)*(s**9.0d0) - &
(37.0d0/2.0d0)*(s**10.0d0) + &
(7.0d0/2.0d0)*(s**11.0d0)
else if (k == 1) then
phi = -(28.0d0)*(s**5.0d0) + &
(154.0d0)*(s**6.0d0) - &
(332.0d0)*(s**7.0d0) + &
(705.0d0/2.0d0)*(s**8.0d0) - &
(185.0d0)*(s**9.0d0) + &
(77.0d0/2.0d0)*(s**10.0d0)
else if (k == 2) then
phi = -(140.0d0)*(s**4.0d0) + &
(924.0d0)*(s**5.0d0) - &
(2324.0d0)*(s**6.0d0) + &
(2820.0d0)*(s**7.0d0) - &
(1665.0d0)*(s**8.0d0) + &
(385.0d0)*(s**9.0d0)
else if (k == 3) then
phi = -(560.0d0)*(s**3.0d0) + &
(4620.0d0)*(s**4.0d0) - &
(13944.0d0)*(s**5.0d0) + &
(19740.0d0)*(s**6.0d0) - &
(13320.0d0)*(s**7.0d0) + &
(3465.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(1680.0d0)*(s**2.0d0) + &
(18480.0d0)*(s**3.0d0) - &
(69720.0d0)*(s**4.0d0) + &
(118440.0d0)*(s**5.0d0) - &
(93240.0d0)*(s**6.0d0) + &
(27720.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(3360.0d0)*s + &
(55440.0d0)*(s**2.0d0) - &
(278880.0d0)*(s**3.0d0) + &
(592200.0d0)*(s**4.0d0) - &
(559440.0d0)*(s**5.0d0) + &
(194040.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(3360.0d0) + &
(110880.0d0)*s - &
(836640.0d0)*(s**2.0d0) + &
(2368800.0d0)*(s**3.0d0) - &
(2797200.0d0)*(s**4.0d0) + &
(1164240.0d0)*(s**5.0d0)
end if
else if (j == 10) then
if (k == 0) then
phi = (7.0d0/24.0d0)*(s**6.0d0) - &
(17.0d0/12.0d0)*(s**7.0d0) + &
(11.0d0/4.0d0)*(s**8.0d0) - &
(8.0d0/3.0d0)*(s**9.0d0) + &
(31.0d0/24.0d0)*(s**10.0d0) - &
(1.0d0/4.0d0)*(s**11.0d0)
else if (k == 1) then
phi = (7.0d0/4.0d0)*(s**5.0d0) - &
(119.0d0/12.0d0)*(s**6.0d0) + &
(22.0d0)*(s**7.0d0) - &
(24.0d0)*(s**8.0d0) + &
(155.0d0/12.0d0)*(s**9.0d0) - &
(11.0d0/4.0d0)*(s**10.0d0)
else if (k == 2) then
phi = (35.0d0/4.0d0)*(s**4.0d0) - &
(119.0d0/2.0d0)*(s**5.0d0) + &
(154.0d0)*(s**6.0d0) - &
(192.0d0)*(s**7.0d0) + &
(465.0d0/4.0d0)*(s**8.0d0) - &
(55.0d0/2.0d0)*(s**9.0d0)
else if (k == 3) then
phi = (35.0d0)*(s**3.0d0) - &
(595.0d0/2.0d0)*(s**4.0d0) + &
(924.0d0)*(s**5.0d0) - &
(1344.0d0)*(s**6.0d0) + &
(930.0d0)*(s**7.0d0) - &
(495.0d0/2.0d0)*(s**8.0d0)
else if (k == 4) then
phi = (105.0d0)*(s**2.0d0) - &
(1190.0d0)*(s**3.0d0) + &
(4620.0d0)*(s**4.0d0) - &
(8064.0d0)*(s**5.0d0) + &
(6510.0d0)*(s**6.0d0) - &
(1980.0d0)*(s**7.0d0)
else if (k == 5) then
phi = (210.0d0)*s - &
(3570.0d0)*(s**2.0d0) + &
(18480.0d0)*(s**3.0d0) - &
(40320.0d0)*(s**4.0d0) + &
(39060.0d0)*(s**5.0d0) - &
(13860.0d0)*(s**6.0d0)
else if (k == 6) then
phi = (210.0d0) - &
(7140.0d0)*s + &
(55440.0d0)*(s**2.0d0) - &
(161280.0d0)*(s**3.0d0) + &
(195300.0d0)*(s**4.0d0) - &
(83160.0d0)*(s**5.0d0)
end if
else if (j == 11) then
if (k == 0) then
phi = -(1.0d0/120.0d0)*(s**6.0d0) + &
(1.0d0/24.0d0)*(s**7.0d0) - &
(1.0d0/12.0d0)*(s**8.0d0) + &
(1.0d0/12.0d0)*(s**9.0d0) - &
(1.0d0/24.0d0)*(s**10.0d0) + &
(1.0d0/120.0d0)*(s**11.0d0)
else if (k == 1) then
phi = -(1.0d0/20.0d0)*(s**5.0d0) + &
(7.0d0/24.0d0)*(s**6.0d0) - &
(2.0d0/3.0d0)*(s**7.0d0) + &
(3.0d0/4.0d0)*(s**8.0d0) - &
(5.0d0/12.0d0)*(s**9.0d0) + &
(11.0d0/120.0d0)*(s**10.0d0)
else if (k == 2) then
phi = -(1.0d0/4.0d0)*(s**4.0d0) + &
(7.0d0/4.0d0)*(s**5.0d0) - &
(14.0d0/3.0d0)*(s**6.0d0) + &
(6.0d0)*(s**7.0d0) - &
(15.0d0/4.0d0)*(s**8.0d0) + &
(11.0d0/12.0d0)*(s**9.0d0)
else if (k == 3) then
phi = -(s**3.0d0) + &
(35.0d0/4.0d0)*(s**4.0d0) - &
(28.0d0)*(s**5.0d0) + &
(42.0d0)*(s**6.0d0) - &
(30.0d0)*(s**7.0d0) + &
(33.0d0/4.0d0)*(s**8.0d0)
else if (k == 4) then
phi = -(3.0d0)*(s**2.0d0) + &
(35.0d0)*(s**3.0d0) - &
(140.0d0)*(s**4.0d0) + &
(252.0d0)*(s**5.0d0) - &
(210.0d0)*(s**6.0d0) + &
(66.0d0)*(s**7.0d0)
else if (k == 5) then
phi = -(6.0d0)*s + &
(105.0d0)*(s**2.0d0) - &
(560.0d0)*(s**3.0d0) + &
(1260.0d0)*(s**4.0d0) - &
(1260.0d0)*(s**5.0d0) + &
(462.0d0)*(s**6.0d0)
else if (k == 6) then
phi = -(6.0d0) + &
(210.0d0)*s - &
(1680.0d0)*(s**2.0d0) + &
(5040.0d0)*(s**3.0d0) - &
(6300.0d0)*(s**4.0d0) + &
(2772.0d0)*(s**5.0d0)
end if
end if
END SUBROUTINE shape_function
SUBROUTINE derivatives(neq,i,x,y,yprime,u,ux,uxx,uxxx,&
uxxxx,uxxxxx,uxxxxxx,utau,rpar)
! return value of u and its spatio-termporal derivatives
! at a point x_i < x < x_i+1
IMPLICIT NONE
INTEGER, INTENT(IN) :: i, neq, x
REAL(kind=8), DIMENSION(neq), INTENT(IN) :: y, yprime
REAL(kind=8), INTENT(OUT) :: u, ux, uxx, uxxx, uxxxx,&
uxxxxx, uxxxxxx, utau
REAL(kind=8), DIMENSION(4+7*12*13), INTENT(IN) :: rpar
REAL(kind=8), PARAMETER :: sone = 0.03376524289842475d0,&
stwo = 0.16939530676686765d0,&
sthree = 0.3806904069584014d0,&
sfour = 0.6193095930415986d0,&
sfive = 0.8306046932331324d0,&
ssix = 0.9662347571015759d0,&
pone = 0.0d0, ptwo = 0.0848880518607158d0,&
pthree = 0.265575603264643d0, pfour = 0.5d0,&
pfive = 0.7344243967353573d0,&
psix = 0.9151119481392833d0, pseven = 1.0d0
REAL(kind=8), DIMENSION(13), PARAMETER :: points = &
[sone, stwo, sthree, sfour, sfive, ssix, pone, ptwo, &
pthree, pfour, pfive, psix, pseven]
REAL(kind=8) :: h, htau
h = y(7*(i+1)) - y(7*i)
htau = yprime(7*(i+1)) - yprime(7*i)
! rpar set up so that rpar(4+1) = phi(0,0,sone), rpar(4+14) =
! phi(0,1,sone), rpar(4+92) = phi(1,0,sone). Use x now to contain
! an integer where 1 to 6 correspond to s's and 7 to 13
! correspond to p's
u = y(7*(i-1)+1)*rpar(4+x) + &
y(7*(i-1)+2)*rpar(4+91+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+x) + &
y(7*i+2)*rpar(4+7*91+x)*h +&
y(7*i+3)*rpar(4+8*91+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+x)*(h**5.0d0)
ux = (y(7*(i-1)+1)*rpar(4+13+x) + &
y(7*(i-1)+2)*rpar(4+91+13+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+13+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+13+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+13+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+13+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+13+x) + &
y(7*i+2)*rpar(4+7*91+13+x)*h +&
y(7*i+3)*rpar(4+8*91+13+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+13+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+13+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+13+x)*(h**5.0d0))/h
uxx = (y(7*(i-1)+1)*rpar(4+2*13+x) + &
y(7*(i-1)+2)*rpar(4+91+2*13+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+2*13+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+2*13+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+2*13+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+2*13+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+2*13+x) + &
y(7*i+2)*rpar(4+7*91+2*13+x)*h +&
y(7*i+3)*rpar(4+8*91+2*13+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+2*13+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+2*13+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+2*13+x)*(h**5.0d0))/(h**2.0d0)
uxxx = (y(7*(i-1)+1)*rpar(4+3*13+x) + &
y(7*(i-1)+2)*rpar(4+91+3*13+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+3*13+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+3*13+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+3*13+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+3*13+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+3*13+x) + &
y(7*i+2)*rpar(4+7*91+3*13+x)*h +&
y(7*i+3)*rpar(4+8*91+3*13+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+3*13+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+3*13+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+3*13+x)*(h**5.0d0))/(h**3.0d0)
uxxxx = (y(7*(i-1)+1)*rpar(4+4*13+x) + &
y(7*(i-1)+2)*rpar(4+91+4*13+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+4*13+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+4*13+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+4*13+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+4*13+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+4*13+x) + &
y(7*i+2)*rpar(4+7*91+4*13+x)*h +&
y(7*i+3)*rpar(4+8*91+4*13+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+4*13+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+4*13+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+4*13+x)*(h**5.0d0))/(h**4.0d0)
uxxxxx = (y(7*(i-1)+1)*rpar(4+5*13+x) + &
y(7*(i-1)+2)*rpar(4+91+5*13+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+5*13+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+5*13+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+5*13+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+5*13+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+5*13+x) + &
y(7*i+2)*rpar(4+7*91+5*13+x)*h +&
y(7*i+3)*rpar(4+8*91+5*13+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+5*13+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+5*13+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+5*13+x)*(h**5.0d0))/(h**5.0d0)
uxxxxxx = (y(7*(i-1)+1)*rpar(4+6*13+x) + &
y(7*(i-1)+2)*rpar(4+91+6*13+x)*h +&
y(7*(i-1)+3)*rpar(4+2*91+6*13+x)*(h**2.0d0) +&
y(7*(i-1)+4)*rpar(4+3*91+6*13+x)*(h**3.0d0) +&
y(7*(i-1)+5)*rpar(4+4*91+6*13+x)*(h**4.0d0) +&
y(7*(i-1)+6)*rpar(4+5*91+6*13+x)*(h**5.0d0) +&
y(7*i+1)*rpar(4+6*91+6*13+x) + &
y(7*i+2)*rpar(4+7*91+6*13+x)*h +&
y(7*i+3)*rpar(4+8*91+6*13+x)*(h**2.0d0) +&
y(7*i+4)*rpar(4+9*91+6*13+x)*(h**3.0d0) +&
y(7*i+5)*rpar(4+10*91+6*13+x)*(h**4.0d0) +&
y(7*i+6)*rpar(4+11*91+6*13+x)*(h**5.0d0))/(h**6.0d0)
utau = yprime(7*(i-1)+1)*rpar(4+x) + &
(yprime(7*(i-1)+2)*h)*rpar(4+91+x) + &
(yprime(7*(i-1)+3)*(h**2.0d0))*rpar(4+2*91+x) + &
(yprime(7*(i-1)+4)*(h**3.0d0))*rpar(4+3*91+x) +&
(yprime(7*(i-1)+5)*(h**4.0d0))*rpar(4+4*91+x) +&
(yprime(7*(i-1)+6)*(h**5.0d0))*rpar(4+5*91+x) +&
yprime(7*i+1)*rpar(4+6*91+x) + &
(yprime(7*i+2)*h)*rpar(4+7*91+x) +&
(yprime(7*i+3)*(h**2.0d0))*rpar(4+8*91+x) +&
(yprime(7*i+4)*(h**3.0d0))*rpar(4+9*91+x) +&
(yprime(7*i+5)*(h**4.0d0))*rpar(4+10*91+x) +&
(yprime(7*i+6)*(h**5.0d0))*rpar(4+11*91+x) -&
ux*(yprime(7*i)+points(x)*htau)
END SUBROUTINE derivatives
SUBROUTINE residual_pde(neq,tau,y,yprime,delta,ires,rpar,ipar)
! Fill the entries of the residual corresponding to the solution and
! its derivatives with the collocation equation (non conservative)
IMPLICIT NONE
INTEGER, INTENT(IN) :: neq
INTEGER :: npts, ii, jj, kk, ll, timetrans, cons, x
REAL(kind=8) :: u, ux, uxx, uxxx, uxxxx, uxxxxx, uxxxxxx, &
utau, vx, xtau, p, g
INTEGER, INTENT(INOUT) :: ires
INTEGER, DIMENSION(*), INTENT(IN) :: ipar
REAL(kind=8) :: h, htau, sund, big
REAL(kind=8), INTENT(IN) :: tau
REAL(kind=8), DIMENSION(neq), INTENT(IN) :: y, yprime
REAL(kind=8), DIMENSION(4+7*12*13), INTENT(IN) :: rpar
REAL(kind=8), DIMENSION(neq), INTENT(INOUT) :: delta
REAL(kind=8), DIMENSION(:), ALLOCATABLE :: fmntr, fsmooth, prmtr
REAL(kind=8), PARAMETER :: sone = 0.03376524289842475d0,&
stwo = 0.16939530676686765d0,&
sthree = 0.3806904069584014d0,&
sfour = 0.6193095930415986d0,&
sfive = 0.8306046932331324d0,&
ssix = 0.9662347571015759d0
REAL(kind=8), DIMENSION(6), PARAMETER :: points = &
[sone, stwo, sthree, sfour, sfive, ssix]
timetrans = ipar(6)
cons = ipar(7)
npts = ipar(4)
p = rpar(1)
ALLOCATE (fmntr(neq),fsmooth(neq),prmtr(neq))
call monitor(neq,y,yprime,fmntr,prmtr,rpar,ipar)
big = 0.0d0
do kk = 1,npts
if (fmntr(7*kk) > big) then
big = fmntr(7*kk)
end if
end do
if (timetrans==1) then
sund = 1.0d0/big
elseif (timetrans==0) then
sund = 1.0d0
end if
if (cons == 0) then
do ii = 1,npts-1
h = y(7*(ii+1))-y(7*ii)
htau = yprime(7*(ii+1)) - yprime(7*ii)
do jj = 1,6
call derivatives(neq,ii,jj,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
! one of these plus the two following lines should be uncommented
! to attempt to stabilize the problem
! call upwinder(neq,ii,jj,y,yprime,u,vx,rpar)
! call lower_order(neq,ii,jj,y,yprime,vx)
xtau = yprime(7*ii) + points(jj)*htau
utau = utau + (ux - vx)*xtau
if (jj < 4) then
delta(7*(ii-1)+3+jj) = utau - sund*g
else
delta(7*ii+jj-3) = utau - sund*g
end if
end do
end do
else if (cons == 1) then
do ii = 1,npts-1
h = y(7*(ii+1))-y(7*ii)
do jj = 1,6
call derivatives(neq,ii,jj,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
if (jj < 4) then
delta(7*(ii-1)+3+jj) = h*utau/sund
else
delta(7*ii+jj-3) = h*utau/sund
end if
end do
do ll = 1,7
if (ll == 1) then
x = 7
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) +&
0.128882066524507657D2*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) -&
0.732825716500196678D0*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) + &
0.164922049039696650D0*g
delta(7*ii+1) = delta(7*ii+1) - &
0.623170625543232604D-1*g
delta(7*ii+2) = delta(7*ii+2) + &
0.304799806699240471D-1*g
delta(7*ii+3) = delta(7*ii+3) - &
0.157386303787899057D-1*g
else if (ll == 2) then
x = 8
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) -&
0.135555128881389990D2*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) +&
0.709951339386726676D1*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) - &
0.658616272480538112D0*g
delta(7*ii+1) = delta(7*ii+1) + &
0.201775206853726796D0*g
delta(7*ii+2) = delta(7*ii+2) - &
0.911735577624964294D-1*g
delta(7*ii+3) = delta(7*ii+3) + &
0.456091312690583006D-1*g
else if (ll == 3) then
x = 9
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) +&
0.823360561753947895D0*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) -&
0.684470480798240999D1*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) + &
0.543104912697367581D1*g
delta(7*ii+1) = delta(7*ii+1) - &
0.575165066473151465D0*g
delta(7*ii+2) = delta(7*ii+2) + &
0.198328593004358011D0*g
delta(7*ii+3) = delta(7*ii+3) - &
0.901243497969793084D-1*g
else if (ll == 4) then
x = 10
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) - &
0.216308174972419803D0*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) + &
0.615652146527092881D0*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) - &
0.537306182570658031D1*g
delta(7*ii+1) = delta(7*ii+1) + &
0.537306182570662916D1*g
delta(7*ii+2) = delta(7*ii+2) - &
0.615652146527116750D0*g
delta(7*ii+3) = delta(7*ii+3) + &
0.216308174972481171D0*g
else if (ll == 5) then
x = 11
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) + &
0.901243497969332896D-1*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) - &
0.198328593004349574D0*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) + &
0.575165066473167785D0*g
delta(7*ii+1) = delta(7*ii+1) - &
0.543104912697373088D1*g
delta(7*ii+2) = delta(7*ii+2) + &
0.684470480798244640D1*g
delta(7*ii+3) = delta(7*ii+3) - &
0.823360561754134634D0*g
else if (ll == 6) then
x = 12
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) - &
0.456091312689924505D-1*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) + &
0.911735577625287091D-1*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) - &
0.201775206853745059D0*g
delta(7*ii+1) = delta(7*ii+1) + &
0.658616272480554432D0*g
delta(7*ii+2) = delta(7*ii+2) - &
0.709951339386726943D1*g
delta(7*ii+3) = delta(7*ii+3) + &
0.135555128881391269D2*g
else if (ll == 7) then
x = 13
call derivatives(neq,ii,x,y,yprime,u,ux,&
uxx,uxxx,uxxxx,uxxxxx,uxxxxxx,utau,rpar)
call def_pde(g,u,ux,uxx,uxxx,uxxxx,uxxxxx,&
uxxxxxx,rpar,ipar)
delta(7*(ii-1)+4) = delta(7*(ii-1)+4) + &
0.157386303787635622D-1*g
delta(7*(ii-1)+5) = delta(7*(ii-1)+5) - &
0.304799806699315723D-1*g
delta(7*(ii-1)+6) = delta(7*(ii-1)+6) + &
0.623170625543236212D-1*g
delta(7*ii+1) = delta(7*ii+1) - &
0.164922049039704727D0*g
delta(7*ii+2) = delta(7*ii+2) + &
0.732825716500154489D0*g
delta(7*ii+3) = delta(7*ii+3) - &
0.128882066524507621D2*g
end if
end do
end do
end if
! Left Boundary Conditions
x = 7