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function [z,z1]=col1()
fixpnt=0
m=[4]
ncomp=1
aleft=1
aright=2
zeta=[1,1,2,2]
ipar=0*ones(1,11)
ipar(3)=1
ipar(4)=2
ipar(5)=2000
ipar(6)=200
ipar(7)=1
ltol=[1,3]
tol=[1.e-11,1.e-11]
res=aleft:0.1:aright
z=bvode(res,ncomp,m,aleft,aright,zeta,ipar,ltol,tol,fixpnt,...
fsub,dfsub,gsub,dgsub,guess)
z1=[]
for x=res,z1=[z1,trusol(x)]; end;
function [df]=dfsub(x,z)
df=[0,0,-6/x**2,-6/x]
function [f]=fsub(x,z)
f=(1 -6*x**2*z(4)-6*x*z(3))/x**3
function [g]=gsub(i,z)
g=[z(1),z(3),z(1),z(3)]
g=g(i)
function [dg]=dgsub(i,z)
dg=[1,0,0,0;0,0,1,0;1,0,0,0;0,0,1,0]
dg=dg(i,:)
function [z,mpar]=guess(x)
// unused here
z=0
mpar=0
function [u]=trusol(x)
u=0*ones(4,1)
u(1) = .25* (10.*log(2.)-3.) * (1.-x) +0.5* (1./x+ (3.+x)*log(x) - x)
u(2) = -.25* (10.*log(2.) - 3.) + .5 * (-1./x/x + log(x) + (3.+x)/x - 1.)
u(3) = .5 * (2./x**3 + 1./x -3./x/x)
u(4) = .5 * (-6./x**4 - 1./x/x + 6./x**3)
function [z,zf]=col2(flag)
ipar=0*ones(1,11)
// define constants, print a heading.
Gamma = 1.1d0
eps = .01d0
dmu = eps
eps4mu = eps**4/dmu
xt = sqrt(2.d0*(Gamma-1.d0)/Gamma)
// define no. of differential equations.
fixpnt=0
iflag=0
ncomp = 2
// orders
m=[2,2]
// interval ends
aleft = 0.d0
aright = 1.d0
// locations of side conditions
zeta=0*ones(1,4)
zeta(1) = 0.d0
zeta(2) = 0.d0
zeta(3) = 1.d0
zeta(4) = 1.d0
// ipar values
// a nonlinear problem
ipar(1) = 1
// 4 collocation points per subinterval
ipar(2) = 4
// initial uniform mesh of 10 subintervals
ipar(3) = 10
ipar(8) = 0
// dimension of real work array fspace is 40000
ipar(5) = 40000
// dimension of integer work array ispace is 2500
ipar(6) = 2500
// (these dimensions of fspace and ispace
// enable colsys to use meshes of up to 192 intervals.)
// print full output.
ipar(7) = 1
// initial approximation for nonlinear iteration is provided
// in solutn
ipar(9) = 1
// a regular problem
ipar(10) = 0
// no fixed points in the mesh
ipar(11) = 0
// tolerances on all components
ipar(4) = 4
ltol=1:4
tol=1.e-5*ones(1,4)
// call colsys
res=aleft:0.05:aright
if flag==1 then
z=bvode(res,ncomp,m,aleft,aright,zeta,ipar,ltol,tol,fixpnt,...
fsub1,dfsub1,gsub1,dgsub1,guess1)
else
z=bvode(res,ncomp,m,aleft,aright,zeta,ipar,ltol,tol,fixpnt,...
'cnf','cndf','cng','cndg','cngu')
end
zf=[ 0.00 0.00000D+00 0.20414D+01 0.10225D-31 -0.90397D+00
0.05 0.10207D+00 0.20414D+01 -0.45265D-01 -0.90794D+00
0.10 0.20414D+00 0.20414D+01 -0.90926D-01 -0.91982D+00
0.15 0.30621D+00 0.20414D+01 -0.13738D+00 -0.93962D+00
0.20 0.40828D+00 0.20414D+01 -0.18502D+00 -0.96735D+00
0.25 0.51035D+00 0.20415D+01 -0.23425D+00 -0.10030D+01
0.30 0.61245D+00 0.20430D+01 -0.28545D+00 -0.10466D+01
0.35 0.71528D+00 0.21066D+01 -0.33905D+00 -0.10992D+01
0.40 0.83213D+00 -0.24518D+00 -0.39612D+00 -0.12054D+01
0.45 0.17751D-01 -0.35755D+01 -0.44540D+00 -0.71354D+00
0.50 0.22512D-01 0.12361D+00 -0.48036D+00 -0.67007D+00
0.55 0.25869D-01 0.48526D-01 -0.51169D+00 -0.58108D+00
0.60 0.28099D-01 0.41111D-01 -0.53831D+00 -0.48234D+00
0.65 0.29911D-01 0.29912D-01 -0.55981D+00 -0.37641D+00
0.70 0.30874D-01 0.55520D-02 -0.57587D+00 -0.26595D+00
0.75 0.30032D-01 -0.45165D-01 -0.58642D+00 -0.15667D+00
0.80 0.25524D-01 -0.14662D+00 -0.59175D+00 -0.60454D-01
0.85 0.13751D-01 -0.34695D+00 -0.59307D+00 -0.14009D-02
0.90 -0.12516D-01 -0.75283D+00 -0.59330D+00 -0.28623D-01
0.95 -0.69427D-01 -0.16508D+01 -0.59906D+00 -0.24811D+00
1.00 0.26514D-13 0.11926D+03 -0.62542D+00 -0.88763D+00 ]
z=z'
zf=zf(:,2:5)
function [z,dmval]=guess1(x)
cons = Gamma * x * (1.d0-.5d0*x*x)
dcons = Gamma * (1.d0 - 1.5d0*x*x)
d2cons = -3.d0 * Gamma * x
if x > xt then z=[0,0,-cons,-dcons]
dmval(2) = -d2cons ;
else z=[ 2.d0 * x, 2 , -2*x+cons,-2+dcons]
dmval(2) = d2cons ;
end
dmval(1) = 0.d0
function [f]=fsub1 (x,z)
f=[0,0]
f(1) = z(1)/x/x - z(2)/x + (z(1) - z(3)*(1.d0-z(1)/x) - ...
Gamma*x*(1.d0-x*x/2.)) / eps4mu
f(2) = z(3)/x/x - z(4)/x + z(1)*(1.d0-z(1)/2.d0/x) / dmu
function [df]=dfsub1 (x, z)
df=0*ones(2,4)
df(1,1) = 1.d0/x/x +(1.d0 + z(3)/x) / eps4mu
df(1,2) = -1.d0/x
df(1,3) = -(1.d0-z(1)/x) / eps4mu
df(1,4) = 0.d0
df(2,1) = (1.d0 - z(1)/x) / dmu
df(2,2) = 0.d0
df(2,3) = 1.d0/x/x
df(2,4) = -1.d0/x
function [g]=gsub1(i, z)
g=[z(1),z(3),z(1), z(4)-0.3d0*z(3)+0.7d0]
g=g(i)
function [dg]=dgsub1 (i, z)
dg=0*ones(4,1)
select i
case 1 then dg(1)=1
case 2 then dg(3)=1
case 3 then dg(1)=1
case 4 then dg(4)=1,dg(3)=-0.3
end
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