Hi, I have problem at this coding. Can you help me?

restart;

eq1 := diff(u(u, t), t) = A[0] + A[1]*cos*omega*t + Beta[1]*[diff(u(u, r), r $ 2) + diff(u(u, r), r)/r];

d

eq1 := --- u(u, t) = A[0] + A[1] cos omega t

dt

[ d ]

[/ 2 \ --- u(u, r)]

[| d | dr ]

+ Beta[1] [|---- u(u, r)| + -----------]

[| 2 | r ]

[\ dr / ]

The*number*of*node*points;

N := 4;

N := 4

The*length*of*domain;

L := 1;

L := 1

BC1 := u(1, t) = 0;

BC1 := u(1, t) = 0

IC1 := u(r, 0) = 0;

IC1 := u(r, 0) = 0

dudt := (u[m + 1] - u[m])/(delta*t);

u[m + 1] - u[m]

dudt := ---------------

delta t

dudr := (u[m + 1, j] - u[m - 1, j])/(2*delta*r);

u[m + 1, j] - u[m - 1, j]

dudr := -------------------------

2 delta r

d2udr2 := (u[m + 1, j] - 2*u[m] + u[m - 1, j])/(delta*r^2);

u[m + 1, j] - 2 u[m] + u[m - 1, j]

d2udr2 := ----------------------------------

2

delta r

Three point forward and backward difference expressions for the derivative are:

Error, unable to parse

Typesetting:-mambiguous(Typesetting:-mambiguous(

Three point forward and backward difference expressions for,

Typesetting:-merror("unable to parse")) the derivative arecolon)

dudrf := (-u[2] + 4*u[1] - 3*u[0])/(2*delta*r);

-u[2] + 4 u[1] - 3 u[0]

dudrf := -----------------------

2 delta r

dudrb := (u[N - 1] - 4*u[N] + 3*u[N + 1])/(2*delta*r);

u[3] - 4 u[4] + 3 u[5]

dudrb := ----------------------

2 delta r

The*governing*equation in finite*difference*form*is;

Eq[m] := subs(diff(u(u, t), t) = dudt, diff(u(u, r), r) = dudr, diff*(u(u, r), r $ 2) = d2udr2, eq1);

u[m + 1] - u[m] [

Eq[m] := --------------- = A[0] + A[1] cos omega t + Beta[1] [

delta t [

[

/ d /u[m + 1, j] - u[m - 1, j]\\ u[m + 1, j] - u[m - 1, j]]

|--- |-------------------------|| + -------------------------]

\ dr \ 2 delta r // 2 ]

2 r delta ]

The*boundary*condition in finite*difference*form*are;

Eq[0] := subs(diff(u(r), r) = dudrf, u(r) = u[0], BC1);

Eq[0] := u(1, t) = 0

The*initial*condition in finite*difference*form*are;

Eq[N + 1] := subs(diff(u(r), r) = dudrb, u(r) = u[0], IC1);

Eq[5] := u(r, 0) = 0

for i to N do

Eq[m] := subs(m = i, Eq[m]);

end do;

u[2] - u[1]

Eq[m] := ----------- = A[0] + A[1] cos omega t + Beta[1] [0]

delta t

u[2] - u[1]

Eq[m] := ----------- = A[0] + A[1] cos omega t + Beta[1] [0]

delta t

u[2] - u[1]

Eq[m] := ----------- = A[0] + A[1] cos omega t + Beta[1] [0]

delta t

u[2] - u[1]

Eq[m] := ----------- = A[0] + A[1] cos omega t + Beta[1] [0]

delta t

The node spacing is given by:

Error, unable to parse

Typesetting:-mambiguous(Typesetting:-mambiguous(

The node spacing is given by,

Typesetting:-merror("unable to parse"))colon)

h := L/(N + 1);

1

h := -

5

eqs := seq(evalm(subs(Beta = 0.25, Eq[i])), i = 0 .. N + 1);

eqs := u(r, 0) = 0, Eq[1], Eq[2], Eq[3], Eq[4], u(r, 0) = 0

vars := seq(u[i], i = 0 .. N + 1);

vars := u[0], u[1], u[2], u[3], u[4], u[5]

soll := fsolve({eqs}, {vars});

Error, (in fsolve) {r, Eq[1], Eq[2], Eq[3], Eq[4]} are in the equation, and are not solved for