I want to solve the following system using PDE Solve command but finding an error. Please help me in this regard. Thanks!
restart; d1 := 1; d2 := 1; AA := 0.2e-2; BB := 0.79e-1; L := 1;
with(PDEtools, casesplit, declare);
PDE1 := diff(u(x, t), t) = d1*(diff(u(x, t), x, x))-u(x, t)*v(x, t)^2+AA*(1-u(x, t)); PDE2 := diff(v(x, t), t) = d1*(diff(v(x, t), x, x))+u(x, t)*v(x, t)^2-BB*v(x, t);
/ 2 \
d | d | 2
PDE1 := --- u(x, t) = |---- u(x, t)| - u(x, t) v(x, t) + 0.002
dt | 2 |
\ dx /
- 0.002 u(x, t)
/ 2 \
d | d | 2
PDE2 := --- v(x, t) = |---- v(x, t)| + u(x, t) v(x, t)
dt | 2 |
\ dx /
- 0.079 v(x, t)
IBC1 := {u(0, t) = 1, u(1, t) = 1, u(x, 0) = 1-(1/2)*sin(Pi*(x-L)/(2*L))^100}; IBC2 := {v(0, t) = 0, v(1, t) = 0, v(x, 0) = (1/4)*sin(Pi*(x-L)/(2*L))^100}; dys1 := {IBC1, IBC2, PDE1, PDE2};
/ / 2 \
| d | d | 2
dys1 := < --- u(x, t) = |---- u(x, t)| - u(x, t) v(x, t) + 0.002
| dt | 2 |
\ \ dx /
- 0.002 u(x, t),
/ 2 \
d | d | 2
--- v(x, t) = |---- v(x, t)| + u(x, t) v(x, t) - 0.079 v(x, t),
dt | 2 |
\ dx /
/ 100
| 1 /1 \
< u(0, t) = 1, u(1, t) = 1, u(x, 0) = 1 - - sin|- Pi (x - 1)|
| 2 \2 /
\
\
|
>,
|
/
/ 100\
| 1 /1 \ |
< v(0, t) = 0, v(1, t) = 0, v(x, 0) = - sin|- Pi (x - 1)| >
| 4 \2 / |
\ /
\
|
>
|
/
pds := pdsolve(dys1, numeric, time = t, range = 0 .. 1);
Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {list, set}, but received time = t
p1 := pds:-plot(t = 0, numpoints = 50);
p2 := pds:-plot(t = 1/8, numpoints = 50, color = blue);
p3 := pds:-plot(t = 1/4, numpoints = 50, color = green);
plots[display]({p1, p2, p3});
Error, `pds` does not evaluate to a module
Error, `pds` does not evaluate to a module
Error, `pds` does not evaluate to a module
Error, (in plots:-display) expecting plot structures but received: {p1, p2, p3}