60 Reputation

0 years, 146 days

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):

Contour Plot from list...

Maple 18

Please, how do plot the contour plot of im(qq) vs Re(qq) from the list below:

qq= [2.106333379+.6286420119*I, 2.106333379-.6286420119*I, 4.654463885, 7.843624703, 10.99193295, 14.13546782, 17.27782732, 20.41978346, 23.56157073, 26.70327712, 29.84494078, 32.98658013, 36.12820481, 39.26982019, 42.41142944, 45.55303453, 48.69463669, 51.83623675, 54.97783528, 58.11943264, 61.26102914]

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