5 years, 8 days

## Plot radial solution in n-sphere...

Maple

Hi all,

R in [0,1] and "t" is a parameter varying in [-1,0[. I started with

restart; n:=3: Sn:=2*Pi^2:
R0:=(n+2)*sqrt(8*Pi/2*Sn); p:=-2*n/(n+2):
U := unapply(piecewise(R<R0, (-t)^p*(R0^2-R^2)/(n+2), 0), R);

## Change of variable...

Maple

Hi all,

I would like to plot a function U(x,t) in an interval [-2,0] such that

U(x,t)=u0(z)+t*u1(z) where  z=x/t,

u0(z)=z^2/3+sqrt(-z) and

diff(u1(z), z)=9/4*(84*(-z)^(11/2)-8*z^7+540*(-z)^(5/2)+324*z^4-324*z)*u1(z)/((z^2+3*sqrt(-z))*(2*(-z)^(3/2)+3)*(8*z^6+66*(-z)^(9/2)-189*z^3+216*(-z)^(3/2)+81))

I used numeric method rkf45 to solve and plot u1(z) with initial condition u1(-2)=1.

I can also use dchange to change variable z to x as variable and t as parameter.

But, I have difficullty to go back to U(x,t).

If someone have any idea.

## How to avoid a singularity...

Hi all,

I deal with the following ODE system which present a singularity when v(x)=0. I want to inject the condition "if v(x)=0 then u(x)=0" as may be a solution to avoid this singularity. If someone could help me to do that. Thanks.

SYS:={u(x)*sqrt(v(x))-diff(v(x),x)*x-2*v(x)=0,2*u(x)*v(x)*diff(v(x),x,x)-u(x)*(diff(v(x),x))^2+2*diff(u(x),x)*v(x)*diff(v(x),x)+v(x)*sqrt(v(x))*(2*x*diff(u(x),x)+6*u(x))=0};

ICS := { u(-2) = 4,   v(-2) = 4, (D(v))(-2) = 0 };
p:= dsolve( SYS union ICS,method=rkf45_dae,numeric,output=listprocedure);
solp := plots[odeplot](p, [[x, u(x)],[x, v(x)]], x = -5 .. 0);
plots[display](solp);

## odeplot for a range of a parameter...

Hi all,

Thanks to help me to plot my result of dsolve for different values of a parameter.

With plots:-animate, I get one curve according to one value of the parameter. But, I need all curves in the same figure.

ws1.mw

Maple 18

Hi all,