hi

I have a linear system with varibles trying to plot 3d the solutions x, y, z

here is my code: linear_var.mw

please any comment might help.

*******************************

restart;

Omega:=10:N:=0.5:M:=sqrt(N(N+1)):

a11:=0.5*(1+2*N)+M*cos(phi):
a12:=-0.5*((1+theta)^3+(1-theta)^3):a13:=-0.5*(N+M*cos(phi))*((1+theta)^3-(1-theta)^3): a21:=M*sin(phi): a22:=(-(1+2*N)+0.5*M*cos(phi))*((1+theta)^3+(1-theta)^3): a23:=-(Omega+0.5*((1+theta)^3-(1-theta)^3)*M*sin(phi)): a31:=0.25*((1+theta)^3-(1-theta)^3): a32:=Omega: a33:=-0.5-(N+0.25)*((1+theta)^3+(1-theta)^3): b1:=-0.5*a31: b2:=0: b3:=0.25+((1+theta)^3+(1-theta)^3)/8:

slove([a11*x+a12*y+a13*z=b1,a21*x+a22*y+a23*z=b2,a31*x+a32*y+a33*z=b3[,[x,y,z]);
Error, unable to match delimiters
Typesetting:-mambiguous(Typesetting:-mambiguous(slovelparlsqba11

  sdotx + a12sdoty + a13sdotzequalsb1commaa21sdotx + a22sdoty + 

  a23sdotzequalsb2commaa31sdotx + a32sdoty + a33sdotzequalsb3lsqb

  comma(xyz)rparsemi, 

  Typesetting:-merror("unable to match delimiters")))

plot3d(x, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed);
plot3d(y, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed); plot3d(z, theta = .1 .. 5, phi = 0 .. 2*Pi, axes = boxed);

I tryning to to plot 3d and then contour plot of the function N vs alpha

This is my try please any comments might help

N_vs_alpha.mw

Hhow can i solve R it says here root of

Calculate.mws

H all expert

first this Expression 

ni := diff(Q(x, t), t)+a*Q*(x, t)*(diff(Q(x, t), x))+b*(diff(Q(x, t), t$3))+d*(diff(Q(x, t), t$5)) = 0

then I want to solve  diff(Q(x, t), t$5) 

diff(Q(x, t), t$5) = solve(ni, diff(Q(x, t), t$5))#eq2

p (x, t) :=H1(t)*Q(x*H2(t), H3(t)) #assumption 

k := diff(p(x, t), t)+a*p(x, t)*(diff(p(x, t), x))+diff(p(x, t), t$3)+d*(diff(p(x, t), t$5))+c*p(x, t) #eq3

r := subs(diff(Q(x, t), t$5), k) #subs eq2 in eq3

i recived error

SUBS1.mw

restart:

sys:={-diff(v(x,t),t)+0.5*p*diff(u(x,t),x,x)+q*u(x,t)*(u(x,t)^2+v(x,t)^2)=0,diff(u(x,t),t)+0.5*p*diff(v(x,t),x,x)+q*v(x,t)*(u(x,t)^2+v(x,t)^2)=0};
        /                      /  2         \
        |/ d         \         | d          |
sys := < |--- u(x, t)| + 0.5 p |---- v(x, t)|
        |\ dt        /         |   2        |
        \                      \ dx         /

               /       2          2\       / d         \
   + q v(x, t) \u(x, t)  + v(x, t) / = 0, -|--- v(x, t)|
                                           \ dt        /

           /  2         \                                      \ 
           | d          |             /       2          2\    | 
   + 0.5 p |---- u(x, t)| + q u(x, t) \u(x, t)  + v(x, t) / = 0 >
           |   2        |                                      | 
           \ dx         /                                      / 
eq1 := diff(u(x,t),t) = u__t(x,t):
eq2 := diff(v(x,t),t) = v__t(x,t):

sys_tmp := subs(eq1, eq2, sys):

sys_new := sys_tmp union {eq1, eq2}:

Boundary conditions:
bc :=
    u(0,t) = 2,
    v(0,t) = 0;
                 bc := u(0, t) = 2, v(0, t) = 0
Initial conditions:
ic :=
    u(x,0) = tanh(2*Pi),
    v(x,0) = tanh(2*Pi),
    u__t(x,0) = 0,
    v__t(x,0) = 0;
 
ic := u(x, 0) = tanh(2 Pi), v(x, 0) = tanh(2 Pi), u__t(x, 0) = 0, 

  v__t(x, 0) = 0
Solve the system:
pdsol := pdsolve(subs(p=1, q=0.5, sys_new), {ic, bc}, numeric);