## Error in dsolve/numeric/bvp...

I've been trying to numerically solve (and plot) this equation. Maple tells me that some matrix is singular - I have no idea, what I can do.

eq := diff(y(x), `\$`(x, 3))-(diff(y(x), x))*(diff(y(x), x))+1 = 0;

cond := (D(y))(0) = 0, (D(y))(1) = 1, ((D@@2)(y))(0) = 0

de := dsolve({cond, eq}, y(x), numeric);

Error, (in dsolve/numeric/bvp) matrix is singular

## Does the principal value of this integral exist?...

I want to make sense of the expression

Int(t^2/ln(t)*exp(-t), t=0..infinity);

The denominator vanishes at t=1.  The singularity at t=1 is not integrable.  I want to see whether the integral is defined in the sense of Cauchy principal value.  Thus, I let

K := Int(t^2/ln(t)*exp(-t), t=0..1-a) + Int(t^2/ln(t)*exp(-t), t=1+a..infinity);

and wish to see whether the following limit exists:

limit(K, a=0, right);

Maple cannot evaluate this.  Nor can I.  Alternatively, we may try:

series(K, a=0);

or

series(K, a=0) assuming a>0, a<1;

In both cases Maple says that it is unable to compute the series.

So my question is: Does the Cauchy principal value exist, and can Maple help one to determine that?

## How to evaluate the double integral?...

I would like to plot the following singular double integral, but I cannot due to singularities...

where x>0, t=0.2 and m=0.2.

I defined f(y) function as f:=y->exp(-(y-4.68)^2/0.4):

I attached my file:
1st_try.mw

Thank you !

## ODE of Lane-Emden type...

=0

 >
 >
 >

plz help me, I m trying to solve homotopy analysis method for lane emden, what additional steps I have to taken in above programming?

## How to solve those ODEs ?...

plz help me, how do i solve singular ODEs of lane Emden type equation for homotopy analysis method in maple? there is arising an arror, invalid fraction

## Finding singular points at blow-up...

Hi,

I try to solve a system of two second order non linear ordinary differential equations using Maple that I expect to find singularities as blow-up points.

So, I would like to know how to compute values of singular points when existing.

ode1: -0.1*diff(u(z),z\$2)+(z-2*diff(v(z)^-1/2,z))*diff(u(z),z)+(3-2*diff(v(z)^-1/2,z\$2)*u(z)=0

ode2: 0.1*diff(v(z),z\$2)+0.01*z*diff(v(z),z)+0.02*v(z)-u(z)*v(z)^1/2=0

Ics: u(0)=0, v(0)=0, D(u)(0)=0, D(v)(0)=0

## obtaining the maximum value of a variable after us...

Dear all,

I have a question regarding the dsolve procedure in Maple. I'm trying to construct a neutron star model using the Tolman-Oppenheimer-Volkoff equation using a polytropic equation of state (EOS) which requires me to solve the ode system:

diff(rho(r),r)=-(rho(r)*(1+K/(5/3-1)*rho(r)^(5/3-1))+K*rho(r)^(5/3))*(4*Pi*r^3*K*rho(r)^(5/3)+m(r))/(K*5/3*rho(r)^(5/3-1)*r*(r-2*m(r)))

diff(m(r),r)=4*Pi*rho(r)*(1+K/(5/3-1)*rho(r)^(5/3-1)

where I have used the EOS P(r)=K*rho(r)^(5/3) and K is a known constant. rho is the density of the star, m it's mass and P the pressure inside the star.

For the initial conditions I have chosen: rho(10^(-10))=rho_0 and m(10^-10)=0. I have chosen r=10^-10 as the innermost point for the integration, since the differential equation for rho is singular at r=0. rho_0 is the central density of the star.

I solve these equations numerically using:

TOV:=dsolve({ode,ics},numeric,output=listprocedure)

where ode is my system of differential equations and ics are my initial conditions. I need now the radius of the star (R_star), which is the maximum value of r, up until which Maple has carried out the integration.

My problem is, I don't know of any efficient way, to do this. What I'm doing currently is defining a procedure TOVr:=rhs(TOV[1]) and I evaluate it at a very high value of r, for which Maple returns me the error message: "Error, (in TOVr) cannot evaluate the solution further right of ..., probably a singularity". I then use the command TOVr('last') to call the maximum value of r and to store it.

I can use the above method, as long as I'm solving the ODEs only for a few different values of rho_0. But I would like to plot m(R_star) for values of rho_0 ranging from 10^(-14) to 10^(-12) in order to find the value of rho_0, for which I can obtain the maximum value for m(R_star). But this requires me to know the value of R_star for every rho_0 and using the above method is not feasible for say hundred different values of rho_0, since I can't write a loop, because it get's terminated as soon as Maple gives me the first error message.

I was thinking of using perhaps the 'events' command in dsolve, to stop the numeric integration once the value for the pressure drops very low, say below 10^(-46), since the radius at which P(r)=0 defines the stellar surface. I tried using:

TOV:=dsolve({ode,ics},numeric, events=[[K*rho(r)^(5/3)-10^(-46),halt]])

but if I try again to evaluate the solution at a large value of r, I get the above error message, and the integration doesn't get canceled, although the value 10^(-46) is bigger than the value for the pressure I would obtain for R_star using TOVr('last') and Maple shouldn't encounter a singularity.

Am I using the 'events' command wrong? And does somebody know of a more efficient method to obtain the maximum value of a variable after carying out a numerical integration using dsolve?

Sorry for the long post and thank you all.

## how to find preimage or kernel of ideal...

i find maple help using regular chain library, but it has ideal source and ideal target,

when compare with singular, seems different, i am not sure singular code whether correct or not.

so, would like to ask how to do this in maple

if you know singular, i would like to know too.

ring r = 32003, (x,y), lp;
setring r;
ideal Z;
ideal i = x-x2-2*x*y+2*x2*y-2*x*y2+y+y2, 1-x2-2*x*y+2*x2*y-2*x*y2+y2;
map phi = r, i;
ideal i1 = preimage(r,phi,Z);
i1;
ideal i2 = preimage(r,i,i);
i2;
ideal i3 = preimage(r,i,Z);
i3;
ideal i4 = preimage(r,Z,i);
i4;

would like to apply to find Cohen Maculay

While(NewKer <> 0)

Mapping = Basis(M – N) ^ K[M]

NewKer = ker(Mapping, M, N)

N = M

M = NewKer

If IsCM(NewKer) = true then

NewKer

End if

Do

## Error, (in dsolve/numeric/bvp) system is singular ...

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);

dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, numeric, output = array([0.]));

Error, (in dsolve/numeric/bvp) system is singular at left endpoint, use midpoint method instead

****************FORMAT TWO ********************************************************

g := (y^2-1)^2; I4 := int(g^4, y = -1 .. 1); I5 := 2*(int(g^3*(diff(g, y, y)), y = -1 .. 1)); I6 := int(g^3*(diff(g, y, y, y, y)), y = -1 .. 1); with(Student[Calculus1]); I10 := ApproximateInt(6/(1-f(x)*g)^2, y = -1 .. 1, method = simpson);
dsys3 := {I4*f(x)^2*(diff(f(x), x, x, x, x))+I5*f(x)^2*(diff(f(x), x, x))+I6*f(x)^3 = I10, f(-1) = 0, f(1) = 0, ((D@@1)(f))(-1) = 0, ((D@@1)(f))(1) = 0};

dsol5 := dsolve(dsys3, method = bvp[midrich], output = array([0.]));
%;
Error, (in dsolve) too many levels of recursion

THANKS A LOT

## Warning, cannot evaluate the solution further righ...

Pleaz i nees help i have probleme withe singularity

 >

Paramétres

 >
 (1.1)

Equation suivant x :

 >
 (2.1)

Equation suivant z :

 >
 (3.1)

Equation suivant y :

 >
 (4.1)

Equation suivant y

 >
 (5.1)

Résolution :

 > CI:= x(0)=0,z(0)=0,theta(0)=0,alpha(0)=0,D(x)(0)=0,D(alpha)(0)=0,D(z)(0)=0,D(theta)(0)=0;
 (6.1)
 > if theta(t) <> 0 then  solution:=dsolve([eq1,eq2,eq3,eq4,CI],numeric,maxfun=0):  odeplot(solution, [[t, x(t)]], t = 0 .. 100, thickness = 2);  odeplot(solution, [[t, z(t)]], t = 0 .. 100, thickness = 2);  odeplot(solution, [[t, theta(t)]], t = 0 .. 100, thickness = 2);  odeplot(solution, [[t, alpha(t)]], t = 0 .. 100, thickness = 2);  #odeplot(solution,[[t,x(t)],[t,alpha(t)],[t,z(t)],[t,theta(t)]], t=0..100, thickness=2);  end ;

thank you !

## The command "singular" returns a wrong result...

s,k,mu,sigma are parameters.k is real number

## Smith Normal Form of a singular matrix...

Hello all,

I have a singular square matrix E (12x12 with its rank of 10). I need to find 2 invertible matrices S and T such that S.E.T is a square diagonal matrix (in Smith Normal form).

Using Maple with the following commands:
>Temp := SmithForm(E);
>Rank(Temp)
Temp is a identity Matrix and Rank of (Temp)  is 12!!! or Rank of (S.E.T) = 12.

However, the determinant of E is less than 10^-29 and rank of E is 10.

## matrix in singular...

Dear all

How to avoid in plot "matrix in singular" in my pde system

`> a1 := -2;                                     -2> b1 := 3;                                      3> c1 := -1;                                     -1> L := 15;                                     15> b := .25;                                    0.25> th := 1.5;                                     1.5> pde := diff(u(x, t), x, x, x, x, t...`

## Algorithm used for singular value decomposition i...

Which algorithm does maple follow for singular value decomposition by command 'SingularValues' in LinearAlgebra Package ?  Is it is QRSVD or divide and conquer or any other   .As far as  I know, MATLAB uses QRSVD.

## Error Maple 15,...

Hello,

I have an error in Maple 15, I dont understand why it doesnt work. I mention that in Maple 13 it works:

The code is

L:=4:

sum(diff( (x^2-1)^l,x\$l),l=0..L);

The error is:

Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation