1 years, 7 days

## Roots of a function complex...

Maple

Hi, please how do I return the roots of a function in the form of I*y. The roots are [-.2381948477, -0.1434221912e-3, 0., 0.1434221912e-3, .2381948477] and I want to return them as [-.2381948477*I, -0.1434221912e-3*I, 0., 0.1434221912e-3*I, .2381948477*I]. I tried to use subs () function but couldn't work.

with(Student[Calculus1]):

soln := Roots(y-0.4646295e-3*tanh(y)+0.1839145082e-2*tanh(y)/(0.6000000000e-3*y^2-0.1840000000e-2), y);

subs(soln, I*y);

## Numerical schemes for second order mixed...

Maple

Is it possible to solve the mixed PDEs below using the method of lines or any other numerical scheme?

B.C:

theta(0,t) = theta(d,t) = 0

v(0,t) = v(d,t) = 0

I.C: theta(z,0) = \thetab*sin(pi/2)*z,  v(z,0) =0 at t =0  for both the initial conditions, where thetab = 0.0001

% parameters.

K3 = 7.5*10^(-12);

eta2 = 0.1361;

alpha2 = -0.1104;

gamma1 = 0.1093;

d = 0.0002;

xi = 0.1;

Note: xi is the controlling parameter. For instance, we can plot theta and v for different values of xi.

I tried matlab but no standard scheme to solve the problem because of the partial^2 theta/partial d partial t term. It would have been possible to use pdepe in Matlab if not for the mixed derivative. Please any help.

Thank you

## Bifurcation of SEIR...

Maple 18

Hi,

Please can someone help me with a sample code for bifurcation? You can use parameter values for the parameters. I'm using maple 18. Below is my model:

 > restart:
 > f__1 := Delta -(psi + mu)*S(t);
 (1)
 > f__2 := psi*S(t) -(delta + mu)*E(t);
 (2)
 > f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);
 (3)
 > f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);
 (4)
 > f__5 := xi*H(t) - mu*R(t);
 (5)
 > f__6 := gamma*X(t)-eta*H(t) - d*D(t);
 (6)
 > f__7 := b*D(t) - b*B(t);
 (7)
 > f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);
 (8)

## How to solve system of equations explici...

Maple

Please I need your assistance. I want to solve for c__4, c__5, c__6, and c__8  from 4 systems of the equation: See my code below:

Since there 4 equations and 4 unknowns, is it possible to get the result explicitly without setting c__6=c__8 as maple did? The solution is at the end of the maple file.

 > ##
 > ###
 > ###
 > restart:
 > f__1 := Delta -(psi + mu)*S(t);
 (1)
 > f__2 := psi*S(t) -(delta + mu)*E(t);
 (2)
 > f__3 := Delta*E(t) -(gamma+gamma__1 + mu)*X(t);
 (3)
 > f__4 := gamma__1*X(t)-(eta + xi + mu)*H(t);
 (4)
 > f__5 := xi*H(t) - mu*R(t);
 (5)
 > f__6 := gamma*X(t)-eta*H(t) - d*D(t);
 (6)
 > f__7 := b*D(t) - b*B(t);
 (7)
 > f__8 := phi__p + sigma*X(t)+eta__1*H(t) +d__1*D(t)+ b__1*B(t) - alpha*P(t);
 (8)
 > S__1 := Delta/mu - a__1*E__1/mu: X__1:= delta*E__1/a__2: H__1 := delta*gamma__1*E__1/a__2*a__3: R__1 := delta*gamma__1*xi*E__1/a__2*a__3*mu: B__1 := 1/b*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: D__1 := 1/d*(gamma*delta/a__2 + delta*eta*gamma__1/a__2*a__3)*E__1: P__1 := (1/alpha)*(delta*sigma/a__2 + delta*eta*gamma__1/a__2*a__3 + (d__1/d - b__1/b)*(delta*gamma/a__2 + delta*eta*gamma__1/a__2*a__3))*E__1 + phi__p/alpha:
 > M__1 := c__1*f__1*(1-S__1/S(t));
 (9)
 > M__2 := c__2*f__2*(1-E__1/E(t));
 (10)
 > M__3 := c__3*f__3*(1-X__1/X(t));
 (11)
 > M__4 :=c__4*f__4*(1-H__1/H(t));
 (12)
 > M__5 := c__5*f__5*(1-R__1/R(t));
 (13)
 > M__6 := c__6*f__6*(1-D__1/D(t));
 (14)
 > M__7 := c__7*f__7*(1-B__1/B(t));
 (15)
 > M__8 := c__8*f__8*(1-P__1/P(t));
 (16)
 > restart:
 > u__1 := (psi+mu)*S__1;
 (17)
 > u__2 := psi*S__1;
 (18)
 > u__3 := delta*E__1;
 (19)
 > u__4 := gamma__1*X__1;
 (20)
 > u__5 := xi*H__1;
 (21)
 > u__6 := gamma*X__1 + eta*H__1;
 (22)
 > u__7 := b*D__1;
 (23)
 > u__8 := phi__p + sigma*X__1+eta__1*H__1 +d__1*D__1+ b__1*B__1;
 (24)
 > M__1 := c__1*(Delta-(psi+mu)*S(t))*(1-(Delta/mu-a__1*E__1/mu)/S(t));
 (25)
 > M__2 := c__2*(psi*S(t)-(delta+mu)*E(t))*(1-E__1/E(t));
 (26)
 > M__3 := c__3*(Delta*E(t)-(gamma+gamma__1+mu)*X(t))*(1-delta*E__1/(a__2*X(t)));
 (27)
 > M__4 := c__4*(gamma__1*X(t)-(eta+xi+mu)*H(t))*(1-delta*gamma__1*E__1*a__3/(a__2*H(t)));
 (28)
 > M__5 := c__5*(xi*H(t)-mu*R(t))*(1-delta*gamma__1*xi*E__1*a__3*mu/(a__2*R(t)));
 (29)
 > M__6 := c__6*(gamma*X(t)-eta*H(t)-d*D(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(d*D(t)));
 (30)
 > M__7 := c__7*(b*D(t)-b*B(t))*(1-(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2)*E__1/(b*B(t)));
 (31)
 > M__8 := c__8*(phi__p+sigma*X(t)+eta__1*H(t)+d__1*D(t)+b__1*B(t)-alpha*P(t))*(1-((delta*sigma/a__2+delta*eta*gamma__1*a__3/a__2+(d__1/d-b__1/b)*(gamma*delta/a__2+delta*eta*gamma__1*a__3/a__2))*E__1/alpha+phi__p/alpha)/P(t));
 (32)
 > J := M__1 + M__2 + M__3 + M__4 + M__5 + M__6 + M__7 + M__8;
 (33)
 > ##
 > L__1 := factor(expand(subs(Delta=u__1, M__1)));
 (34)
 > L__2 := expand(subs((delta+mu)*E(t)=u__2, M__2));
 (35)
 > L__3 := expand(subs((gamma+gamma__1+mu)*X(t)=u__3, M__3));
 (36)
 > L__4 := expand(subs((eta+xi+mu)*H(t)=u__4, M__4));
 (37)
 > L__5 := expand(subs(mu*R(t)=u__5, M__5));
 (38)
 > L__6 := expand(subs(d*D(t)=u__6, M__6));
 (39)
 > L__7 := expand(subs(b*B(t)=u__7, M__7));
 (40)
 > L__8 := expand(subs(alpha*P(t)=u__8, M__8));
 (41)
 > L := L__1 + L__2 + L__3 + L__4 + L__5 + L__6 + L__7 + L__8;
 (42)
 > ## Collecting the coefficients of X, H, D, B and E
 > k__1 := coeff(L,X(t));
 (43)
 > k__2 := coeff(L,H(t));
 (44)
 > k__3 := coeff(L, D(t));
 (45)
 > k__4 := coeff(L, B(t));
 (46)
 > k__5 := coeff(L, E(t));
 (47)
 > ##
 > ## L terms that not coeffiecient X, H, D, B and E
 > W__12 := coeff(L, X(t), 0):
 > W__1 := coeff(W__12, H(t), 0):
 > W__11 := coeff(W__1, D(t), 0):
 > W__12 := coeff(W__11, B(t), 0):
 > k__6 := coeff(W__12, E(t), 0);
 (48)
 > ## from k__5, c__3 = 0 and choose c__1 = c__2 and c__3 =c__7
 > c__3 := 0:  c__7:=0:
 > k__1;
 (49)
 > k__2;
 (50)
 > k__3;
 (51)
 > k__4;
 (52)
 > ## Also choose
 > sys := solve({k__1=0, k__2 =0, k__3=0, k__4=0}, [c__4,c__5, c__6, c__8]);
 (53)
 > #
 > #
 >

## Pairing 2 lists into another list and us...

Maple

Hi please, how can I pair two lists and form another list?

P := [.6286420119, -.6286420119, 0., 0., 0., 0., 0., 0., 0., 0., 0.]

Q = [2.106333379, 2.106333379, 4.654463885, 7.843624703, 10.99193295, 14.13546782, 17.27782732, 20.41978346, 23.56157073, 26.70327712, 29.84494078]

I want to pair them into something like this:

W := [ [.6286420119,2.106333379], [-.6286420119,  2.106333379] ... ]

Then use pointplot(W) and  display(seq(pointplot(W[j], j = 1 .. 20), insequence = true):

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