2 years, 1 days

## How I can solve this problem to plot...

Maple

Hello, I am trying to plot this one and I did not get the graph, I don't know where the problem. Could you please help. thank you

restart;
with(plots):

alpha := 0.005;
beta := 0.01;
beta := 0.01

mu := 0.005;
mu := 0.005

m := 0.003;
m := 0.003

u := 0.3;
u := 0.3

w := 0.3;
w := 0.3

v := 1;
v := 1

gamma = 0.1;
gamma = 0.1

Gamma := 0.01;
Gamma := 0.01

Eq := sigma^4 + sigma^3*[2*(mu*v + mu) + 2*alpha - beta*(u + w) + 2*beta*v] + sigma^2*[4*mu*m + 2*alpha*(2*mu + m) + alpha^2 - 2*beta*v(mu - 2*m) - 2*beta*(u + w)*(mu + m) + alpha*beta*(4*beta + (-u - w)) - beta^2*v*(u + w - v) + k^2*(Gamma^2 + gamma^2)] + sigma*[2*alpha*mu*(2*m - beta*(u + w)) + 2*alpha^2*(beta*v + mu) - 4*beta*mu*m*(u + w + v) + 4*alpha*beta*v*(mu + m) - 2*beta^2*v*(u + w) + 2*beta^2*v^2*(m + alpha) - alpha*beta^2*v*(u + w) + 2*Gamma^2*beta*v*k^2 + 2*k^2*(Gamma^2*mu + gamma^2*m) + gamma^2*k^2*(2*alpha - beta*(u + w))] + [Gamma^2*k^2*(2*beta*mu*v + gamma^2) + Gamma^2*beta^2*k^2*v*(Gamma*v - gamma*(u + w)) - beta*gamma^2*k^2*(u + w)*(alpha + 2*m) + alpha^2*(beta^2*v^2 + gamma^2*k^2) + 2*alpha*beta^2*v*(v*m - mu*(u + w)) + 4*beta*mu*m*v*(alpha - beta*(u + w))];
p1 := implicitplot(Eq, k = 0 .. 10, sigma = -0.1 .. 0.1);
4
Eq := sigma

3
+ sigma  [2 mu v + 2 alpha + 2 mu - beta (u + w) + 2 beta v] +

2 [                                   2
sigma  [4 mu m + 2 alpha (2 mu + m) + alpha

- 2 beta v(mu - 2 m) - 2 beta (u + w) (mu + m)

2
+ alpha beta (4 beta - u - w) - beta  v (u + w - v)

2 /     2        2\]         [
+ k  \Gamma  + gamma /] + sigma [2 alpha mu (2 m

2
- beta (u + w)) + 2 alpha  (beta v + mu)

- 4 beta mu m (u + w + v) + 4 alpha beta v (mu + m)

2                   2  2
- 2 beta  v (u + w) + 2 beta  v  (m + alpha)

2                    2         2
- alpha beta  v (u + w) + 2 Gamma  beta v k

2 /     2           2  \
+ 2 k  \Gamma  mu + gamma  m/

2  2                         ]   [     2  2 /
+ gamma  k  (2 alpha - beta (u + w))] + [Gamma  k  \2 beta mu v

2\        2     2  2
+ gamma / + Gamma  beta  k  v (Gamma v - gamma (u + w))

2  2
- beta gamma  k  (u + w) (alpha + 2 m)

2 /    2  2        2  2\
+ alpha  \beta  v  + gamma  k /

2
+ 2 alpha beta  v (v m - mu (u + w))

]
+ 4 beta mu m v (alpha - beta (u + w))]

[k1,0], [k2,0], [k3,0], ...) , where k_{n}=2*n*Pi/L and the domain [0,L]
L:=10.0;
p2:=pointplot([seq([2*n*Pi/L,0],n=0..10)],color=red,symbolsize=15):
display(p1,p2);
L := 10.0

/            /     4
display\implicitplot\sigma

3
+ sigma  [2 mu v + 2 alpha + 2 mu - beta (u + w) + 2 beta v] +

2 [                                   2
sigma  [4 mu m + 2 alpha (2 mu + m) + alpha

- 2 beta v(mu - 2 m) - 2 beta (u + w) (mu + m)

2
+ alpha beta (4 beta - u - w) - beta  v (u + w - v)

2 /     2        2\]         [
+ k  \Gamma  + gamma /] + sigma [2 alpha mu (2 m

2
- beta (u + w)) + 2 alpha  (beta v + mu)

- 4 beta mu m (u + w + v) + 4 alpha beta v (mu + m)

2                   2  2
- 2 beta  v (u + w) + 2 beta  v  (m + alpha)

2                    2         2
- alpha beta  v (u + w) + 2 Gamma  beta v k

2 /     2           2  \
+ 2 k  \Gamma  mu + gamma  m/

2  2                         ]   [     2  2 /
+ gamma  k  (2 alpha - beta (u + w))] + [Gamma  k  \2 beta mu v

2\        2     2  2
+ gamma / + Gamma  beta  k  v (Gamma v - gamma (u + w))

2  2
- beta gamma  k  (u + w) (alpha + 2 m)

2 /    2  2        2  2\
+ alpha  \beta  v  + gamma  k /

2
+ 2 alpha beta  v (v m - mu (u + w))

]
+ 4 beta mu m v (alpha - beta (u + w))], k = 0 .. 10,

\
sigma = -0.1 .. 0.1/, pointplot([[0., 0], [0.6283185308, 0],

[1.256637062, 0], [1.884955592, 0], [2.513274124, 0],

[3.141592654, 0], [3.769911184, 0], [4.398229716, 0],

[5.026548246, 0], [5.654866778, 0], [6.283185308, 0]],

\
color = red, symbolsize = 15)/

## How I can plot a function with complex t...

Maple

Could please help me what is the problem of the following and how I can plot it

restart;
with(LinearAlgebra);
with(plots, implicitplot);
M := Matrix([[sigma + Gamma*ik + 0.5 + 0.5*tanh(c - v) + beta*v, -0.5 + 0.5*tanh(c - v), 0.5*(w - u)*sech^2*(c - v) - beta*u], [-0.5 - 0.5*tanh(c - v), sigma - i*k*Gamma + 0.5 + 0.5*tanh(c - v) + beta*v, 0.5*(u - w)*sech^2*(c - v) - beta*w], [-beta*v, -beta*v, sigma - beta*alpha*(u + w)]]):

Eq := Determinant(M):

alpha := 0.1;
beta := 0.01;
mu := 0.5;
u := 0.5;
v := 1;
Gamma := 0.1;
c := 2;
w := 0.5;

p1r := evalc(Re(Eq)):

p1 := implicitplot(Eq, k = 0 .. 10, sigma = -0.01 .. 0.01);
Error, (in plots/implicitplot) invalid input: the following extra unknowns were found in the input expression: {i, ik}

## plot discrete point...

Maple

Hello , I need to plot the following on the same axes of implicit plot where discrete wavenumbers k1, k2, k3 on the same set of axes (the wavenumbers are points [k1,0], [k2,0], [k3,0], ...) , where k_{n}=2*n*Pi/L and the domain [0,L]

Could you please help , I couldn't do. Thank you

restart;
with(plots, implicitplot);
alpha := 0.1;
beta := 0.1;
mu := 0.5;
u := 0.5;
v := 1;
gamma = 0.1;
alpha := 0.1

beta := 0.1

mu := 0.5

u := 0.5

v := 1

gamma = 0.1

Eq := -2*sigma*alpha*beta*mu*u - sigma*alpha*beta^2*u*v - 2.0*mu*alpha*beta^2*u*v - gamma^2*k^2*alpha*beta*u + beta*sigma^2*v + sigma^3 + 2*mu*sigma^2 - alpha*beta*sigma^2*u + sigma*beta^2*u*v + gamma^2*k^2*sigma + 2.0*mu*beta*sigma*v + 2.0*mu*beta^2*u*v;
2  2              2
Eq := 0.0995 sigma + 0.004500 - 0.005 gamma  k  + 1.095 sigma

3        2  2
+ sigma  + gamma  k  sigma

implicitplot(Eq, k = 0 .. 10, sigma = -0.1 .. 0.1);

## How I solve hyperbolic of epidemic spre...

Maple

The following is my code, it is working but when I add third model in pde1 , it is not working .

Note that: u :people move to right,w: move to left,v: infected people and stationary(not move)

please help me to reconize the problem

restart;
with(PDEtools);
with(plots);
pde1 := {diff(u(x, t), t) + Gamma*diff(u(x, t), x) = mu(w - u) - 0.5*beta*v*(w - u) - beta*u*v, diff(w(x, t), t) - Gamma*diff(w(x, t), x) = mu(u - w) - 0.5*beta*v*(u - w) - beta*w*v,diff(v(x,t),t)=beta*u*v-alpha*v};

IBC1 := {u(0, t) = 0, u(x, 0) = exp(-200*(x - 0.4)^2), w(1, t) = 0, w(x, 0) = exp(-200*(x - 0.6)^2),v(x,0)=0,v(0,t)=sin(t)};
mu := 0.0009;
Gamma := 10;alpha:=1;beta:=0.1

pds1 := pdsolve(pde1, IBC1, numeric, time = t, range = 0 .. 1, spacestep = 0.001);

## how do i solve the following problem in ...

hi daer

i am trying to run the following but error came

acually the boundry conditions are periodic

x=linspace(0,1,50);
t=linspace(0,1,50);
m=0;
eqn=@(x,t,u,dudx)transistorPDE(x,t,u,dudx,C);
ic=@(x)transistorIC(x,C);
sol=pdepe((m,eqn,ic,transistorBC,x,t);
function [c,f,s]=transistorPDE(x,t,u,dudx,C)
a=0.1;
c=1;
f=0;
s=-a*dudx;
end
function u0=transistorIC(x,C)
L=1;
u0=exp(-(x-L/2)^2);
end
function [pl,ql,pr,qr]=transistorBC(xl,ul,xr,ur,t)
pl=ul;
ql=0;
pr=pl;
qr=0;
end

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