How can I export data from the plot? Following is my Maple code.
restart;
with(PDEtools);
v_0 := 1;
vstar := 10;
r_0 := 1;
k := 0.1;
m := 0.1;
PDE := diff(v(r, t), t) = k*(diff(v(r, t), r, r) + diff(v(r, t), r)/r);
/ d \
/ 2 \ 0.1 |--- v(r, t)|
d | d | \ dr /
PDE := --- v(r, t) = 0.1 |---- v(r, t)| + -----------------
dt | 2 | r
\ dr /
ans := pdsolve(PDE, HINT = f(r)*g(t));
/
|
|
ans := Typesetting:-mcomplete|vApplyFunction(rt)equalsf__1
|
|
\
//
||
||DifferentialD
ApplyFunction(r) f__2ApplyFunction(t) where ||--------------
||DifferentialDt
\\
f__2ApplyFunction(t)equals0.1 f__2ApplyFunction(t) _c[1]
2
DifferentialD
--------------- f__1ApplyFunction(r)equals1. f__1ApplyFunction(
2
DifferentialDr
/DifferentialD \//
1. |-------------- f__1ApplyFunction(r)|||
\DifferentialDr /||
r) _c[1] - ----------------------------------------||,
r ||
\\
/[ / [ /
|[ | [ |
|[ | [ |
Typesetting:-_Hold|[PDESolStruc|v(r, t) = f__1(r) f__2(t), [<
|[ | [ |
|[ | [ |
\[ \ [ \
d
--- f__2(t) = 0.1 f__2(t) _c[1],
dt
/ d \\ ]\]\\
2 1. |--- f__1(r)|| ]|]||
d \ dr /| ]|]||
---- f__1(r) = 1. f__1(r) _c[1] - ---------------- >]|]||
2 r | ]|]||
dr | ]|]||
/ ]/]//
build(ans);
/1 \ / (1/2) \
v(r, t) = c__3 exp|-- _c[1] t| c__1 BesselJ\0, (-_c[1]) r/
\10 /
/1 \ / (1/2) \
+ c__3 exp|-- _c[1] t| c__2 BesselY\0, (-_c[1]) r/
\10 /
design;
BC1 := eval(v(r, t) - v_0 = 0, r = 20);
BC1 := v(20, t) - 1 = 0
BC2 := D[1](v)(0, t) = 0;
BC2 := D[1](v)(0, t) = 0
NULL;
IC := v(r, 0) = v_0 + (vstar - v_0)*exp(-0.5*(r - r_0)^2/m^2)/(m*sqrt(2*Pi));
(1/2) / 2\
IC := v(r, 0) = 1 + 25.38853126 2 exp\-50. (r - 1) /
conds := {BC1, BC2, IC};
/
conds := { v(20, t) - 1 = 0,
\
(1/2) / 2\
v(r, 0) = 1 + 25.38853126 2 exp\-50. (r - 1) /,
\
D[1](v)(0, t) = 0 }
/
answer:=pdsolve(PDE,conds,HINT=);
Error, invalid =
Typesetting:-mambiguous(answerAssignpdsolveApplyFunction(PDEcomma
condscommaTypesetting:-mambiguous(HINTequalslowast,
Typesetting:-merror("invalid =")))semi)
u := r -> v_0 + (vstar - v_0)*exp((-1)*0.5*(r - r_0)^2/m^2)/(m*sqrt(2*Pi));
u := proc (r) options operator, arrow, function_assign;
v_0+(vstar-v_0)*exp(-.5*(r-r_0)^2/m^2)/(m*sqrt(2*Pi)) end proc
plot(u(r), r = 0 .. 10);
conds := {BC1, BC2, IC};
/
conds := { v(20, t) - 1 = 0,
\
(1/2) / 2\
v(r, 0) = 1 + 25.38853126 2 exp\-50. (r - 1) /,
\
D[1](v)(0, t) = 0 }
/
BCs := {BC1, BC2};
BCs := {v(20, t) - 1 = 0, D[1](v)(0, t) = 0}
pde_solve = pdsolve(PDE, BCs, IC);
solution := pdsolve(PDE, conds, numeric);
solution := _m1440390954528
t1 = 0 .. 10;
r1 = 0 .. 10;
solution, t1, r1;
solution, t1, r1
sol := pdsolve(PDE, conds, numeric, time = t, range = 0 .. 20, spacestep = 0.1, timestep = 0.1);
sol := _m1440421519392
sol:-animate(t = 0 .. 20, frames = 100);
M := sol:-value();
sol:-plot3d(r = 0 .. 10, t = 0 .. 20);
